Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [805,2,Mod(22,805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(805, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("805.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 805 = 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 805.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.42795736271\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(72\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 183.7 | ||
Character | \(\chi\) | \(=\) | 805.183 |
Dual form | 805.2.l.a.22.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/805\mathbb{Z}\right)^\times\).
\(n\) | \(162\) | \(281\) | \(346\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60576 | + | 1.60576i | −1.13545 | + | 1.13545i | −0.146190 | + | 0.989257i | \(0.546701\pi\) |
−0.989257 | + | 0.146190i | \(0.953299\pi\) | |||||||
\(3\) | 0.871410 | + | 0.871410i | 0.503109 | + | 0.503109i | 0.912403 | − | 0.409294i | \(-0.134225\pi\) |
−0.409294 | + | 0.912403i | \(0.634225\pi\) | |||||||
\(4\) | − | 3.15695i | − | 1.57848i | ||||||
\(5\) | −2.02341 | − | 0.951750i | −0.904895 | − | 0.425636i | ||||
\(6\) | −2.79856 | −1.14251 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 1.85780 | + | 1.85780i | 0.656830 | + | 0.656830i | ||||
\(9\) | − | 1.48129i | − | 0.493763i | ||||||
\(10\) | 4.77740 | − | 1.72083i | 1.51075 | − | 0.544173i | ||||
\(11\) | 5.11689i | 1.54280i | 0.636350 | + | 0.771401i | \(0.280443\pi\) | ||||
−0.636350 | + | 0.771401i | \(0.719557\pi\) | |||||||
\(12\) | 2.75100 | − | 2.75100i | 0.794146 | − | 0.794146i | ||||
\(13\) | −1.17759 | − | 1.17759i | −0.326604 | − | 0.326604i | 0.524690 | − | 0.851294i | \(-0.324181\pi\) |
−0.851294 | + | 0.524690i | \(0.824181\pi\) | |||||||
\(14\) | −2.27089 | −0.606922 | ||||||||
\(15\) | −0.933852 | − | 2.59258i | −0.241120 | − | 0.669402i | ||||
\(16\) | 0.347548 | 0.0868870 | ||||||||
\(17\) | −5.05771 | − | 5.05771i | −1.22668 | − | 1.22668i | −0.965214 | − | 0.261461i | \(-0.915796\pi\) |
−0.261461 | − | 0.965214i | \(-0.584204\pi\) | |||||||
\(18\) | 2.37860 | + | 2.37860i | 0.560641 | + | 0.560641i | ||||
\(19\) | 0.177493 | 0.0407197 | 0.0203599 | − | 0.999793i | \(-0.493519\pi\) | ||||
0.0203599 | + | 0.999793i | \(0.493519\pi\) | |||||||
\(20\) | −3.00463 | + | 6.38780i | −0.671856 | + | 1.42836i | ||||
\(21\) | 1.23236i | 0.268923i | ||||||||
\(22\) | −8.21652 | − | 8.21652i | −1.75177 | − | 1.75177i | ||||
\(23\) | −1.70842 | − | 4.48121i | −0.356231 | − | 0.934398i | ||||
\(24\) | 3.23780i | 0.660914i | ||||||||
\(25\) | 3.18834 | + | 3.85155i | 0.637669 | + | 0.770311i | ||||
\(26\) | 3.78186 | 0.741683 | ||||||||
\(27\) | 3.90504 | − | 3.90504i | 0.751525 | − | 0.751525i | ||||
\(28\) | 2.23230 | − | 2.23230i | 0.421866 | − | 0.421866i | ||||
\(29\) | − | 5.33033i | − | 0.989817i | −0.868945 | − | 0.494908i | \(-0.835202\pi\) | ||
0.868945 | − | 0.494908i | \(-0.164798\pi\) | |||||||
\(30\) | 5.66262 | + | 2.66353i | 1.03385 | + | 0.486291i | ||||
\(31\) | 7.33641 | 1.31766 | 0.658829 | − | 0.752293i | \(-0.271052\pi\) | ||||
0.658829 | + | 0.752293i | \(0.271052\pi\) | |||||||
\(32\) | −4.27367 | + | 4.27367i | −0.755485 | + | 0.755485i | ||||
\(33\) | −4.45891 | + | 4.45891i | −0.776197 | + | 0.776197i | ||||
\(34\) | 16.2430 | 2.78565 | ||||||||
\(35\) | −0.757775 | − | 2.10375i | −0.128087 | − | 0.355599i | ||||
\(36\) | −4.67636 | −0.779394 | ||||||||
\(37\) | −0.899035 | − | 0.899035i | −0.147800 | − | 0.147800i | 0.629334 | − | 0.777135i | \(-0.283328\pi\) |
−0.777135 | + | 0.629334i | \(0.783328\pi\) | |||||||
\(38\) | −0.285012 | + | 0.285012i | −0.0462351 | + | 0.0462351i | ||||
\(39\) | − | 2.05232i | − | 0.328635i | ||||||
\(40\) | −1.99092 | − | 5.52723i | −0.314792 | − | 0.873932i | ||||
\(41\) | 9.00707 | 1.40667 | 0.703334 | − | 0.710860i | \(-0.251694\pi\) | ||||
0.703334 | + | 0.710860i | \(0.251694\pi\) | |||||||
\(42\) | −1.97888 | − | 1.97888i | −0.305348 | − | 0.305348i | ||||
\(43\) | 4.95163 | − | 4.95163i | 0.755117 | − | 0.755117i | −0.220313 | − | 0.975429i | \(-0.570708\pi\) |
0.975429 | + | 0.220313i | \(0.0707078\pi\) | |||||||
\(44\) | 16.1538 | 2.43528 | ||||||||
\(45\) | −1.40982 | + | 2.99725i | −0.210163 | + | 0.446804i | ||||
\(46\) | 9.93910 | + | 4.45245i | 1.46544 | + | 0.656477i | ||||
\(47\) | 8.09939 | − | 8.09939i | 1.18142 | − | 1.18142i | 0.202040 | − | 0.979377i | \(-0.435243\pi\) |
0.979377 | − | 0.202040i | \(-0.0647571\pi\) | |||||||
\(48\) | 0.302857 | + | 0.302857i | 0.0437136 | + | 0.0437136i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −11.3044 | − | 1.06496i | −1.59869 | − | 0.150608i | ||||
\(51\) | − | 8.81468i | − | 1.23430i | ||||||
\(52\) | −3.71759 | + | 3.71759i | −0.515537 | + | 0.515537i | ||||
\(53\) | −6.96493 | + | 6.96493i | −0.956706 | + | 0.956706i | −0.999101 | − | 0.0423949i | \(-0.986501\pi\) |
0.0423949 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(54\) | 12.5411i | 1.70663i | ||||||||
\(55\) | 4.87000 | − | 10.3536i | 0.656671 | − | 1.39607i | ||||
\(56\) | 2.62732i | 0.351090i | ||||||||
\(57\) | 0.154669 | + | 0.154669i | 0.0204865 | + | 0.0204865i | ||||
\(58\) | 8.55925 | + | 8.55925i | 1.12388 | + | 1.12388i | ||||
\(59\) | − | 0.00127673i | − | 0.000166216i | −1.00000 | 8.31079e-5i | \(-0.999974\pi\) | |||
1.00000 | 8.31079e-5i | \(-2.64541e-5\pi\) | ||||||||
\(60\) | −8.18466 | + | 2.94813i | −1.05663 | + | 0.380602i | ||||
\(61\) | − | 3.67196i | − | 0.470146i | −0.971978 | − | 0.235073i | \(-0.924467\pi\) | ||
0.971978 | − | 0.235073i | \(-0.0755329\pi\) | |||||||
\(62\) | −11.7805 | + | 11.7805i | −1.49613 | + | 1.49613i | ||||
\(63\) | 1.04743 | − | 1.04743i | 0.131964 | − | 0.131964i | ||||
\(64\) | − | 13.0299i | − | 1.62874i | ||||||
\(65\) | 1.26197 | + | 3.50351i | 0.156528 | + | 0.434557i | ||||
\(66\) | − | 14.3199i | − | 1.76266i | ||||||
\(67\) | −6.28020 | − | 6.28020i | −0.767248 | − | 0.767248i | 0.210373 | − | 0.977621i | \(-0.432532\pi\) |
−0.977621 | + | 0.210373i | \(0.932532\pi\) | |||||||
\(68\) | −15.9670 | + | 15.9670i | −1.93628 | + | 1.93628i | ||||
\(69\) | 2.41624 | − | 5.39371i | 0.290881 | − | 0.649327i | ||||
\(70\) | 4.59494 | + | 2.16132i | 0.549200 | + | 0.258327i | ||||
\(71\) | −15.2707 | −1.81230 | −0.906150 | − | 0.422957i | \(-0.860992\pi\) | ||||
−0.906150 | + | 0.422957i | \(0.860992\pi\) | |||||||
\(72\) | 2.75193 | − | 2.75193i | 0.324318 | − | 0.324318i | ||||
\(73\) | 2.76584 | + | 2.76584i | 0.323717 | + | 0.323717i | 0.850191 | − | 0.526474i | \(-0.176486\pi\) |
−0.526474 | + | 0.850191i | \(0.676486\pi\) | |||||||
\(74\) | 2.88728 | 0.335639 | ||||||||
\(75\) | −0.577928 | + | 6.13464i | −0.0667333 | + | 0.708367i | ||||
\(76\) | − | 0.560338i | − | 0.0642752i | ||||||
\(77\) | −3.61819 | + | 3.61819i | −0.412331 | + | 0.412331i | ||||
\(78\) | 3.29555 | + | 3.29555i | 0.373147 | + | 0.373147i | ||||
\(79\) | 7.06344 | 0.794700 | 0.397350 | − | 0.917667i | \(-0.369930\pi\) | ||||
0.397350 | + | 0.917667i | \(0.369930\pi\) | |||||||
\(80\) | −0.703231 | − | 0.330779i | −0.0786236 | − | 0.0369822i | ||||
\(81\) | 2.36192 | 0.262435 | ||||||||
\(82\) | −14.4632 | + | 14.4632i | −1.59720 | + | 1.59720i | ||||
\(83\) | 7.31116 | − | 7.31116i | 0.802504 | − | 0.802504i | −0.180982 | − | 0.983486i | \(-0.557928\pi\) |
0.983486 | + | 0.180982i | \(0.0579277\pi\) | |||||||
\(84\) | 3.89050 | 0.424489 | ||||||||
\(85\) | 5.42013 | + | 15.0475i | 0.587895 | + | 1.63213i | ||||
\(86\) | 15.9023i | 1.71479i | ||||||||
\(87\) | 4.64490 | − | 4.64490i | 0.497986 | − | 0.497986i | ||||
\(88\) | −9.50614 | + | 9.50614i | −1.01336 | + | 1.01336i | ||||
\(89\) | 9.74973 | 1.03347 | 0.516735 | − | 0.856146i | \(-0.327147\pi\) | ||||
0.516735 | + | 0.856146i | \(0.327147\pi\) | |||||||
\(90\) | −2.54904 | − | 7.07671i | −0.268693 | − | 0.745950i | ||||
\(91\) | − | 1.66536i | − | 0.174577i | ||||||
\(92\) | −14.1470 | + | 5.39342i | −1.47493 | + | 0.562303i | ||||
\(93\) | 6.39302 | + | 6.39302i | 0.662925 | + | 0.662925i | ||||
\(94\) | 26.0114i | 2.68287i | ||||||||
\(95\) | −0.359141 | − | 0.168929i | −0.0368471 | − | 0.0173318i | ||||
\(96\) | −7.44824 | −0.760183 | ||||||||
\(97\) | −3.61536 | − | 3.61536i | −0.367084 | − | 0.367084i | 0.499329 | − | 0.866413i | \(-0.333580\pi\) |
−0.866413 | + | 0.499329i | \(0.833580\pi\) | |||||||
\(98\) | −1.60576 | − | 1.60576i | −0.162207 | − | 0.162207i | ||||
\(99\) | 7.57960 | 0.761778 | ||||||||
\(100\) | 12.1592 | − | 10.0655i | 1.21592 | − | 1.00655i | ||||
\(101\) | −6.96295 | −0.692840 | −0.346420 | − | 0.938080i | \(-0.612603\pi\) | ||||
−0.346420 | + | 0.938080i | \(0.612603\pi\) | |||||||
\(102\) | 14.1543 | + | 14.1543i | 1.40148 | + | 1.40148i | ||||
\(103\) | −9.94408 | + | 9.94408i | −0.979819 | + | 0.979819i | −0.999800 | − | 0.0199809i | \(-0.993639\pi\) |
0.0199809 | + | 0.999800i | \(0.493639\pi\) | |||||||
\(104\) | − | 4.37543i | − | 0.429047i | ||||||
\(105\) | 1.17290 | − | 2.49356i | 0.114463 | − | 0.243347i | ||||
\(106\) | − | 22.3680i | − | 2.17258i | ||||||
\(107\) | 2.45830 | + | 2.45830i | 0.237653 | + | 0.237653i | 0.815878 | − | 0.578225i | \(-0.196254\pi\) |
−0.578225 | + | 0.815878i | \(0.696254\pi\) | |||||||
\(108\) | −12.3280 | − | 12.3280i | −1.18627 | − | 1.18627i | ||||
\(109\) | −1.65584 | −0.158600 | −0.0793002 | − | 0.996851i | \(-0.525269\pi\) | ||||
−0.0793002 | + | 0.996851i | \(0.525269\pi\) | |||||||
\(110\) | 8.80528 | + | 24.4454i | 0.839551 | + | 2.33078i | ||||
\(111\) | − | 1.56686i | − | 0.148719i | ||||||
\(112\) | 0.245754 | + | 0.245754i | 0.0232215 | + | 0.0232215i | ||||
\(113\) | 8.11245 | − | 8.11245i | 0.763155 | − | 0.763155i | −0.213736 | − | 0.976891i | \(-0.568563\pi\) |
0.976891 | + | 0.213736i | \(0.0685634\pi\) | |||||||
\(114\) | −0.496725 | −0.0465226 | ||||||||
\(115\) | −0.808160 | + | 10.6933i | −0.0753613 | + | 0.997156i | ||||
\(116\) | −16.8276 | −1.56240 | ||||||||
\(117\) | −1.74435 | + | 1.74435i | −0.161265 | + | 0.161265i | ||||
\(118\) | 0.00205012 | + | 0.00205012i | 0.000188729 | + | 0.000188729i | ||||
\(119\) | − | 7.15268i | − | 0.655685i | ||||||
\(120\) | 3.08158 | − | 6.55139i | 0.281308 | − | 0.598057i | ||||
\(121\) | −15.1826 | −1.38024 | ||||||||
\(122\) | 5.89629 | + | 5.89629i | 0.533825 | + | 0.533825i | ||||
\(123\) | 7.84885 | + | 7.84885i | 0.707707 | + | 0.707707i | ||||
\(124\) | − | 23.1607i | − | 2.07989i | ||||||
\(125\) | −2.78560 | − | 10.8278i | −0.249151 | − | 0.968465i | ||||
\(126\) | 3.36385i | 0.299675i | ||||||||
\(127\) | 9.37869 | − | 9.37869i | 0.832224 | − | 0.832224i | −0.155597 | − | 0.987821i | \(-0.549730\pi\) |
0.987821 | + | 0.155597i | \(0.0497301\pi\) | |||||||
\(128\) | 12.3756 | + | 12.3756i | 1.09386 | + | 1.09386i | ||||
\(129\) | 8.62980 | 0.759812 | ||||||||
\(130\) | −7.65223 | − | 3.59938i | −0.671145 | − | 0.315687i | ||||
\(131\) | 4.26187 | 0.372361 | 0.186180 | − | 0.982516i | \(-0.440389\pi\) | ||||
0.186180 | + | 0.982516i | \(0.440389\pi\) | |||||||
\(132\) | 14.0766 | + | 14.0766i | 1.22521 | + | 1.22521i | ||||
\(133\) | 0.125507 | + | 0.125507i | 0.0108828 | + | 0.0108828i | ||||
\(134\) | 20.1690 | 1.74234 | ||||||||
\(135\) | −11.6181 | + | 4.18486i | −0.999927 | + | 0.360175i | ||||
\(136\) | − | 18.7924i | − | 1.61143i | ||||||
\(137\) | 10.7577 | + | 10.7577i | 0.919090 | + | 0.919090i | 0.996963 | − | 0.0778736i | \(-0.0248131\pi\) |
−0.0778736 | + | 0.996963i | \(0.524813\pi\) | |||||||
\(138\) | 4.78112 | + | 12.5409i | 0.406996 | + | 1.06756i | ||||
\(139\) | 8.20058i | 0.695564i | 0.937575 | + | 0.347782i | \(0.113065\pi\) | ||||
−0.937575 | + | 0.347782i | \(0.886935\pi\) | |||||||
\(140\) | −6.64145 | + | 2.39226i | −0.561305 | + | 0.202183i | ||||
\(141\) | 14.1158 | 1.18876 | ||||||||
\(142\) | 24.5212 | − | 24.5212i | 2.05777 | − | 2.05777i | ||||
\(143\) | 6.02559 | − | 6.02559i | 0.503885 | − | 0.503885i | ||||
\(144\) | − | 0.514819i | − | 0.0429016i | ||||||
\(145\) | −5.07314 | + | 10.7854i | −0.421301 | + | 0.895680i | ||||
\(146\) | −8.88258 | −0.735127 | ||||||||
\(147\) | −0.871410 | + | 0.871410i | −0.0718727 | + | 0.0718727i | ||||
\(148\) | −2.83821 | + | 2.83821i | −0.233300 | + | 0.233300i | ||||
\(149\) | −20.0963 | −1.64636 | −0.823178 | − | 0.567784i | \(-0.807801\pi\) | ||||
−0.823178 | + | 0.567784i | \(0.807801\pi\) | |||||||
\(150\) | −8.92276 | − | 10.7788i | −0.728541 | − | 0.880085i | ||||
\(151\) | 16.3331 | 1.32917 | 0.664585 | − | 0.747212i | \(-0.268608\pi\) | ||||
0.664585 | + | 0.747212i | \(0.268608\pi\) | |||||||
\(152\) | 0.329746 | + | 0.329746i | 0.0267459 | + | 0.0267459i | ||||
\(153\) | −7.49193 | + | 7.49193i | −0.605687 | + | 0.605687i | ||||
\(154\) | − | 11.6199i | − | 0.936359i | ||||||
\(155\) | −14.8445 | − | 6.98243i | −1.19234 | − | 0.560842i | ||||
\(156\) | −6.47909 | −0.518743 | ||||||||
\(157\) | −10.6024 | − | 10.6024i | −0.846166 | − | 0.846166i | 0.143486 | − | 0.989652i | \(-0.454169\pi\) |
−0.989652 | + | 0.143486i | \(0.954169\pi\) | |||||||
\(158\) | −11.3422 | + | 11.3422i | −0.902339 | + | 0.902339i | ||||
\(159\) | −12.1386 | −0.962655 | ||||||||
\(160\) | 12.7148 | − | 4.57990i | 1.00520 | − | 0.362073i | ||||
\(161\) | 1.96066 | − | 4.37674i | 0.154522 | − | 0.344935i | ||||
\(162\) | −3.79268 | + | 3.79268i | −0.297981 | + | 0.297981i | ||||
\(163\) | −7.21699 | − | 7.21699i | −0.565278 | − | 0.565278i | 0.365524 | − | 0.930802i | \(-0.380890\pi\) |
−0.930802 | + | 0.365524i | \(0.880890\pi\) | |||||||
\(164\) | − | 28.4349i | − | 2.22039i | ||||||
\(165\) | 13.2660 | − | 4.77842i | 1.03275 | − | 0.371999i | ||||
\(166\) | 23.4800i | 1.82240i | ||||||||
\(167\) | −11.5383 | + | 11.5383i | −0.892862 | + | 0.892862i | −0.994792 | − | 0.101929i | \(-0.967498\pi\) |
0.101929 | + | 0.994792i | \(0.467498\pi\) | |||||||
\(168\) | −2.28947 | + | 2.28947i | −0.176637 | + | 0.176637i | ||||
\(169\) | − | 10.2266i | − | 0.786659i | ||||||
\(170\) | −32.8661 | − | 15.4593i | −2.52072 | − | 1.18567i | ||||
\(171\) | − | 0.262919i | − | 0.0201059i | ||||||
\(172\) | −15.6321 | − | 15.6321i | −1.19193 | − | 1.19193i | ||||
\(173\) | −4.88923 | − | 4.88923i | −0.371722 | − | 0.371722i | 0.496382 | − | 0.868104i | \(-0.334661\pi\) |
−0.868104 | + | 0.496382i | \(0.834661\pi\) | |||||||
\(174\) | 14.9172i | 1.13087i | ||||||||
\(175\) | −0.468960 | + | 4.97796i | −0.0354500 | + | 0.376298i | ||||
\(176\) | 1.77837i | 0.134049i | ||||||||
\(177\) | 0.00111255 | − | 0.00111255i | 8.36246e−5 | − | 8.36246e-5i | ||||
\(178\) | −15.6558 | + | 15.6558i | −1.17345 | + | 1.17345i | ||||
\(179\) | − | 9.43066i | − | 0.704881i | −0.935834 | − | 0.352440i | \(-0.885352\pi\) | ||
0.935834 | − | 0.352440i | \(-0.114648\pi\) | |||||||
\(180\) | 9.46218 | + | 4.45073i | 0.705269 | + | 0.331738i | ||||
\(181\) | − | 22.3549i | − | 1.66163i | −0.556551 | − | 0.830813i | \(-0.687876\pi\) | ||
0.556551 | − | 0.830813i | \(-0.312124\pi\) | |||||||
\(182\) | 2.67418 | + | 2.67418i | 0.198223 | + | 0.198223i | ||||
\(183\) | 3.19978 | − | 3.19978i | 0.236534 | − | 0.236534i | ||||
\(184\) | 5.15128 | − | 11.4991i | 0.379757 | − | 0.847724i | ||||
\(185\) | 0.963457 | + | 2.67477i | 0.0708347 | + | 0.196653i | ||||
\(186\) | −20.5314 | −1.50543 | ||||||||
\(187\) | 25.8798 | − | 25.8798i | 1.89252 | − | 1.89252i | ||||
\(188\) | −25.5694 | − | 25.5694i | −1.86484 | − | 1.86484i | ||||
\(189\) | 5.52256 | 0.401707 | ||||||||
\(190\) | 0.847956 | − | 0.305435i | 0.0615172 | − | 0.0221586i | ||||
\(191\) | − | 7.38066i | − | 0.534046i | −0.963690 | − | 0.267023i | \(-0.913960\pi\) | ||
0.963690 | − | 0.267023i | \(-0.0860399\pi\) | |||||||
\(192\) | 11.3544 | − | 11.3544i | 0.819433 | − | 0.819433i | ||||
\(193\) | −9.22954 | − | 9.22954i | −0.664357 | − | 0.664357i | 0.292047 | − | 0.956404i | \(-0.405664\pi\) |
−0.956404 | + | 0.292047i | \(0.905664\pi\) | |||||||
\(194\) | 11.6108 | 0.833608 | ||||||||
\(195\) | −1.95330 | + | 4.15268i | −0.139879 | + | 0.297380i | ||||
\(196\) | 3.15695 | 0.225497 | ||||||||
\(197\) | −9.00339 | + | 9.00339i | −0.641465 | + | 0.641465i | −0.950916 | − | 0.309450i | \(-0.899855\pi\) |
0.309450 | + | 0.950916i | \(0.399855\pi\) | |||||||
\(198\) | −12.1710 | + | 12.1710i | −0.864958 | + | 0.864958i | ||||
\(199\) | 14.2467 | 1.00992 | 0.504962 | − | 0.863142i | \(-0.331507\pi\) | ||||
0.504962 | + | 0.863142i | \(0.331507\pi\) | |||||||
\(200\) | −1.23211 | + | 13.0787i | −0.0871232 | + | 0.924803i | ||||
\(201\) | − | 10.9453i | − | 0.772019i | ||||||
\(202\) | 11.1809 | − | 11.1809i | 0.786682 | − | 0.786682i | ||||
\(203\) | 3.76911 | − | 3.76911i | 0.264540 | − | 0.264540i | ||||
\(204\) | −27.8275 | −1.94832 | ||||||||
\(205\) | −18.2250 | − | 8.57248i | −1.27289 | − | 0.598728i | ||||
\(206\) | − | 31.9357i | − | 2.22507i | ||||||
\(207\) | −6.63797 | + | 2.53067i | −0.461371 | + | 0.175894i | ||||
\(208\) | −0.409268 | − | 0.409268i | −0.0283777 | − | 0.0283777i | ||||
\(209\) | 0.908214i | 0.0628225i | ||||||||
\(210\) | 2.12068 | + | 5.88747i | 0.146341 | + | 0.406274i | ||||
\(211\) | −24.0833 | −1.65796 | −0.828982 | − | 0.559276i | \(-0.811079\pi\) | ||||
−0.828982 | + | 0.559276i | \(0.811079\pi\) | |||||||
\(212\) | 21.9880 | + | 21.9880i | 1.51014 | + | 1.51014i | ||||
\(213\) | −13.3070 | − | 13.3070i | −0.911784 | − | 0.911784i | ||||
\(214\) | −7.89490 | −0.539684 | ||||||||
\(215\) | −14.7319 | + | 5.30644i | −1.00471 | + | 0.361897i | ||||
\(216\) | 14.5095 | 0.987249 | ||||||||
\(217\) | 5.18762 | + | 5.18762i | 0.352159 | + | 0.352159i | ||||
\(218\) | 2.65888 | − | 2.65888i | 0.180082 | − | 0.180082i | ||||
\(219\) | 4.82036i | 0.325730i | ||||||||
\(220\) | −32.6857 | − | 15.3744i | −2.20367 | − | 1.03654i | ||||
\(221\) | 11.9118i | 0.801274i | ||||||||
\(222\) | 2.51600 | + | 2.51600i | 0.168863 | + | 0.168863i | ||||
\(223\) | −4.29281 | − | 4.29281i | −0.287468 | − | 0.287468i | 0.548610 | − | 0.836078i | \(-0.315157\pi\) |
−0.836078 | + | 0.548610i | \(0.815157\pi\) | |||||||
\(224\) | −6.04388 | −0.403824 | ||||||||
\(225\) | 5.70526 | − | 4.72286i | 0.380351 | − | 0.314857i | ||||
\(226\) | 26.0534i | 1.73304i | ||||||||
\(227\) | 5.29397 | + | 5.29397i | 0.351373 | + | 0.351373i | 0.860620 | − | 0.509247i | \(-0.170076\pi\) |
−0.509247 | + | 0.860620i | \(0.670076\pi\) | |||||||
\(228\) | 0.488284 | − | 0.488284i | 0.0323374 | − | 0.0323374i | ||||
\(229\) | −2.13155 | −0.140857 | −0.0704284 | − | 0.997517i | \(-0.522437\pi\) | ||||
−0.0704284 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(230\) | −15.8732 | − | 18.4686i | −1.04665 | − | 1.21779i | ||||
\(231\) | −6.30585 | −0.414895 | ||||||||
\(232\) | 9.90266 | − | 9.90266i | 0.650141 | − | 0.650141i | ||||
\(233\) | 10.5794 | + | 10.5794i | 0.693080 | + | 0.693080i | 0.962908 | − | 0.269828i | \(-0.0869670\pi\) |
−0.269828 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(234\) | − | 5.60202i | − | 0.366216i | ||||||
\(235\) | −24.0969 | + | 8.67976i | −1.57191 | + | 0.566205i | ||||
\(236\) | −0.00403057 | −0.000262368 | ||||||||
\(237\) | 6.15516 | + | 6.15516i | 0.399820 | + | 0.399820i | ||||
\(238\) | 11.4855 | + | 11.4855i | 0.744496 | + | 0.744496i | ||||
\(239\) | − | 20.2127i | − | 1.30745i | −0.756731 | − | 0.653726i | \(-0.773205\pi\) | ||
0.756731 | − | 0.653726i | \(-0.226795\pi\) | |||||||
\(240\) | −0.324558 | − | 0.901046i | −0.0209502 | − | 0.0581623i | ||||
\(241\) | − | 3.93449i | − | 0.253443i | −0.991938 | − | 0.126721i | \(-0.959555\pi\) | ||
0.991938 | − | 0.126721i | \(-0.0404454\pi\) | |||||||
\(242\) | 24.3797 | − | 24.3797i | 1.56718 | − | 1.56718i | ||||
\(243\) | −9.65692 | − | 9.65692i | −0.619492 | − | 0.619492i | ||||
\(244\) | −11.5922 | −0.742114 | ||||||||
\(245\) | 0.951750 | − | 2.02341i | 0.0608051 | − | 0.129271i | ||||
\(246\) | −25.2068 | −1.60713 | ||||||||
\(247\) | −0.209014 | − | 0.209014i | −0.0132992 | − | 0.0132992i | ||||
\(248\) | 13.6295 | + | 13.6295i | 0.865477 | + | 0.865477i | ||||
\(249\) | 12.7420 | 0.807494 | ||||||||
\(250\) | 21.8598 | + | 12.9138i | 1.38254 | + | 0.816741i | ||||
\(251\) | 13.0565i | 0.824118i | 0.911157 | + | 0.412059i | \(0.135190\pi\) | ||||
−0.911157 | + | 0.412059i | \(0.864810\pi\) | |||||||
\(252\) | −3.30669 | − | 3.30669i | −0.208302 | − | 0.208302i | ||||
\(253\) | 22.9299 | − | 8.74182i | 1.44159 | − | 0.549594i | ||||
\(254\) | 30.1199i | 1.88989i | ||||||||
\(255\) | −8.38937 | + | 17.8357i | −0.525363 | + | 1.11691i | ||||
\(256\) | −13.6848 | −0.855301 | ||||||||
\(257\) | −0.762361 | + | 0.762361i | −0.0475547 | + | 0.0475547i | −0.730484 | − | 0.682930i | \(-0.760706\pi\) |
0.682930 | + | 0.730484i | \(0.260706\pi\) | |||||||
\(258\) | −13.8574 | + | 13.8574i | −0.862725 | + | 0.862725i | ||||
\(259\) | − | 1.27143i | − | 0.0790027i | ||||||
\(260\) | 11.0604 | − | 3.98398i | 0.685938 | − | 0.247076i | ||||
\(261\) | −7.89575 | −0.488735 | ||||||||
\(262\) | −6.84355 | + | 6.84355i | −0.422796 | + | 0.422796i | ||||
\(263\) | −8.16290 | + | 8.16290i | −0.503346 | + | 0.503346i | −0.912476 | − | 0.409130i | \(-0.865832\pi\) |
0.409130 | + | 0.912476i | \(0.365832\pi\) | |||||||
\(264\) | −16.5675 | −1.01966 | ||||||||
\(265\) | 20.7217 | − | 7.46400i | 1.27293 | − | 0.458510i | ||||
\(266\) | −0.403068 | −0.0247137 | ||||||||
\(267\) | 8.49601 | + | 8.49601i | 0.519948 | + | 0.519948i | ||||
\(268\) | −19.8263 | + | 19.8263i | −1.21108 | + | 1.21108i | ||||
\(269\) | − | 16.1342i | − | 0.983717i | −0.870675 | − | 0.491859i | \(-0.836318\pi\) | ||
0.870675 | − | 0.491859i | \(-0.163682\pi\) | |||||||
\(270\) | 11.9360 | − | 25.3758i | 0.726404 | − | 1.54432i | ||||
\(271\) | 28.0822 | 1.70587 | 0.852937 | − | 0.522013i | \(-0.174819\pi\) | ||||
0.852937 | + | 0.522013i | \(0.174819\pi\) | |||||||
\(272\) | −1.75780 | − | 1.75780i | −0.106582 | − | 0.106582i | ||||
\(273\) | 1.45121 | − | 1.45121i | 0.0878314 | − | 0.0878314i | ||||
\(274\) | −34.5485 | −2.08715 | ||||||||
\(275\) | −19.7080 | + | 16.3144i | −1.18844 | + | 0.983796i | ||||
\(276\) | −17.0277 | − | 7.62795i | −1.02495 | − | 0.459149i | ||||
\(277\) | −9.30858 | + | 9.30858i | −0.559298 | + | 0.559298i | −0.929108 | − | 0.369809i | \(-0.879423\pi\) |
0.369809 | + | 0.929108i | \(0.379423\pi\) | |||||||
\(278\) | −13.1682 | − | 13.1682i | −0.789776 | − | 0.789776i | ||||
\(279\) | − | 10.8673i | − | 0.650611i | ||||||
\(280\) | 2.50055 | − | 5.31613i | 0.149437 | − | 0.317700i | ||||
\(281\) | 10.6158i | 0.633287i | 0.948545 | + | 0.316644i | \(0.102556\pi\) | ||||
−0.948545 | + | 0.316644i | \(0.897444\pi\) | |||||||
\(282\) | −22.6666 | + | 22.6666i | −1.34978 | + | 1.34978i | ||||
\(283\) | −1.39498 | + | 1.39498i | −0.0829228 | + | 0.0829228i | −0.747352 | − | 0.664429i | \(-0.768675\pi\) |
0.664429 | + | 0.747352i | \(0.268675\pi\) | |||||||
\(284\) | 48.2089i | 2.86067i | ||||||||
\(285\) | −0.165752 | − | 0.460166i | −0.00981833 | − | 0.0272579i | ||||
\(286\) | 19.3514i | 1.14427i | ||||||||
\(287\) | 6.36896 | + | 6.36896i | 0.375948 | + | 0.375948i | ||||
\(288\) | 6.33054 | + | 6.33054i | 0.373031 | + | 0.373031i | ||||
\(289\) | 34.1609i | 2.00946i | ||||||||
\(290\) | −9.17257 | − | 25.4651i | −0.538632 | − | 1.49536i | ||||
\(291\) | − | 6.30092i | − | 0.369366i | ||||||
\(292\) | 8.73164 | − | 8.73164i | 0.510980 | − | 0.510980i | ||||
\(293\) | 0.213491 | − | 0.213491i | 0.0124723 | − | 0.0124723i | −0.700843 | − | 0.713315i | \(-0.747193\pi\) |
0.713315 | + | 0.700843i | \(0.247193\pi\) | |||||||
\(294\) | − | 2.79856i | − | 0.163215i | ||||||
\(295\) | −0.00121513 | + | 0.00258334i | −7.07473e−5 | + | 0.000150408i | ||||
\(296\) | − | 3.34045i | − | 0.194160i | ||||||
\(297\) | 19.9817 | + | 19.9817i | 1.15945 | + | 1.15945i | ||||
\(298\) | 32.2700 | − | 32.2700i | 1.86935 | − | 1.86935i | ||||
\(299\) | −3.26520 | + | 7.28884i | −0.188832 | + | 0.421525i | ||||
\(300\) | 19.3668 | + | 1.82449i | 1.11814 | + | 0.105337i | ||||
\(301\) | 7.00266 | 0.403627 | ||||||||
\(302\) | −26.2271 | + | 26.2271i | −1.50920 | + | 1.50920i | ||||
\(303\) | −6.06759 | − | 6.06759i | −0.348574 | − | 0.348574i | ||||
\(304\) | 0.0616874 | 0.00353802 | ||||||||
\(305\) | −3.49478 | + | 7.42986i | −0.200111 | + | 0.425432i | ||||
\(306\) | − | 24.0605i | − | 1.37545i | ||||||
\(307\) | −21.1411 | + | 21.1411i | −1.20659 | + | 1.20659i | −0.234461 | + | 0.972126i | \(0.575332\pi\) |
−0.972126 | + | 0.234461i | \(0.924668\pi\) | |||||||
\(308\) | 11.4225 | + | 11.4225i | 0.650855 | + | 0.650855i | ||||
\(309\) | −17.3307 | −0.985912 | ||||||||
\(310\) | 35.0489 | − | 12.6247i | 1.99065 | − | 0.717034i | ||||
\(311\) | 22.9906 | 1.30368 | 0.651838 | − | 0.758358i | \(-0.273998\pi\) | ||||
0.651838 | + | 0.758358i | \(0.273998\pi\) | |||||||
\(312\) | 3.81280 | − | 3.81280i | 0.215857 | − | 0.215857i | ||||
\(313\) | 20.7186 | − | 20.7186i | 1.17109 | − | 1.17109i | 0.189136 | − | 0.981951i | \(-0.439431\pi\) |
0.981951 | − | 0.189136i | \(-0.0605688\pi\) | |||||||
\(314\) | 34.0500 | 1.92155 | ||||||||
\(315\) | −3.11627 | + | 1.12248i | −0.175582 | + | 0.0632448i | ||||
\(316\) | − | 22.2990i | − | 1.25442i | ||||||
\(317\) | 12.5484 | − | 12.5484i | 0.704787 | − | 0.704787i | −0.260647 | − | 0.965434i | \(-0.583936\pi\) |
0.965434 | + | 0.260647i | \(0.0839360\pi\) | |||||||
\(318\) | 19.4917 | − | 19.4917i | 1.09304 | − | 1.09304i | ||||
\(319\) | 27.2747 | 1.52709 | ||||||||
\(320\) | −12.4012 | + | 26.3648i | −0.693249 | + | 1.47384i | ||||
\(321\) | 4.28438i | 0.239131i | ||||||||
\(322\) | 3.87965 | + | 10.1764i | 0.216204 | + | 0.567106i | ||||
\(323\) | −0.897710 | − | 0.897710i | −0.0499499 | − | 0.0499499i | ||||
\(324\) | − | 7.45646i | − | 0.414248i | ||||||
\(325\) | 0.780988 | − | 8.29010i | 0.0433214 | − | 0.459852i | ||||
\(326\) | 23.1776 | 1.28369 | ||||||||
\(327\) | −1.44291 | − | 1.44291i | −0.0797933 | − | 0.0797933i | ||||
\(328\) | 16.7333 | + | 16.7333i | 0.923941 | + | 0.923941i | ||||
\(329\) | 11.4543 | 0.631494 | ||||||||
\(330\) | −13.6290 | + | 28.9750i | −0.750251 | + | 1.59502i | ||||
\(331\) | 10.6802 | 0.587035 | 0.293517 | − | 0.955954i | \(-0.405174\pi\) | ||||
0.293517 | + | 0.955954i | \(0.405174\pi\) | |||||||
\(332\) | −23.0810 | − | 23.0810i | −1.26673 | − | 1.26673i | ||||
\(333\) | −1.33173 | + | 1.33173i | −0.0729784 | + | 0.0729784i | ||||
\(334\) | − | 37.0556i | − | 2.02759i | ||||||
\(335\) | 6.73021 | + | 18.6846i | 0.367711 | + | 1.02085i | ||||
\(336\) | 0.428304i | 0.0233659i | ||||||||
\(337\) | −8.15510 | − | 8.15510i | −0.444237 | − | 0.444237i | 0.449196 | − | 0.893433i | \(-0.351710\pi\) |
−0.893433 | + | 0.449196i | \(0.851710\pi\) | |||||||
\(338\) | 16.4215 | + | 16.4215i | 0.893210 | + | 0.893210i | ||||
\(339\) | 14.1385 | 0.767900 | ||||||||
\(340\) | 47.5042 | − | 17.1111i | 2.57628 | − | 0.927979i | ||||
\(341\) | 37.5396i | 2.03288i | ||||||||
\(342\) | 0.422186 | + | 0.422186i | 0.0228292 | + | 0.0228292i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 18.3982 | 0.991966 | ||||||||
\(345\) | −10.0225 | + | 8.61402i | −0.539593 | + | 0.463763i | ||||
\(346\) | 15.7019 | 0.844140 | ||||||||
\(347\) | −15.7945 | + | 15.7945i | −0.847891 | + | 0.847891i | −0.989870 | − | 0.141978i | \(-0.954654\pi\) |
0.141978 | + | 0.989870i | \(0.454654\pi\) | |||||||
\(348\) | −14.6637 | − | 14.6637i | −0.786059 | − | 0.786059i | ||||
\(349\) | 14.9580i | 0.800683i | 0.916366 | + | 0.400341i | \(0.131108\pi\) | ||||
−0.916366 | + | 0.400341i | \(0.868892\pi\) | |||||||
\(350\) | −7.24039 | − | 8.74647i | −0.387015 | − | 0.467518i | ||||
\(351\) | −9.19706 | −0.490903 | ||||||||
\(352\) | −21.8679 | − | 21.8679i | −1.16556 | − | 1.16556i | ||||
\(353\) | −5.37387 | − | 5.37387i | −0.286022 | − | 0.286022i | 0.549483 | − | 0.835505i | \(-0.314825\pi\) |
−0.835505 | + | 0.549483i | \(0.814825\pi\) | |||||||
\(354\) | 0.00357299i | 0.000189903i | ||||||||
\(355\) | 30.8988 | + | 14.5339i | 1.63994 | + | 0.771379i | ||||
\(356\) | − | 30.7795i | − | 1.63131i | ||||||
\(357\) | 6.23292 | − | 6.23292i | 0.329881 | − | 0.329881i | ||||
\(358\) | 15.1434 | + | 15.1434i | 0.800354 | + | 0.800354i | ||||
\(359\) | −25.9955 | −1.37199 | −0.685995 | − | 0.727606i | \(-0.740633\pi\) | ||||
−0.685995 | + | 0.727606i | \(0.740633\pi\) | |||||||
\(360\) | −8.18743 | + | 2.94912i | −0.431515 | + | 0.155432i | ||||
\(361\) | −18.9685 | −0.998342 | ||||||||
\(362\) | 35.8967 | + | 35.8967i | 1.88669 | + | 1.88669i | ||||
\(363\) | −13.2303 | − | 13.2303i | −0.694409 | − | 0.694409i | ||||
\(364\) | −5.25747 | −0.275566 | ||||||||
\(365\) | −2.96403 | − | 8.22881i | −0.155144 | − | 0.430716i | ||||
\(366\) | 10.2762i | 0.537144i | ||||||||
\(367\) | −6.61291 | − | 6.61291i | −0.345191 | − | 0.345191i | 0.513123 | − | 0.858315i | \(-0.328488\pi\) |
−0.858315 | + | 0.513123i | \(0.828488\pi\) | |||||||
\(368\) | −0.593760 | − | 1.55744i | −0.0309519 | − | 0.0811870i | ||||
\(369\) | − | 13.3421i | − | 0.694560i | ||||||
\(370\) | −5.84213 | − | 2.74797i | −0.303718 | − | 0.142860i | ||||
\(371\) | −9.84989 | −0.511381 | ||||||||
\(372\) | 20.1825 | − | 20.1825i | 1.04641 | − | 1.04641i | ||||
\(373\) | 9.58468 | − | 9.58468i | 0.496276 | − | 0.496276i | −0.414001 | − | 0.910277i | \(-0.635869\pi\) |
0.910277 | + | 0.414001i | \(0.135869\pi\) | |||||||
\(374\) | 83.1136i | 4.29770i | ||||||||
\(375\) | 7.00802 | − | 11.8628i | 0.361893 | − | 0.612593i | ||||
\(376\) | 30.0940 | 1.55198 | ||||||||
\(377\) | −6.27693 | + | 6.27693i | −0.323278 | + | 0.323278i | ||||
\(378\) | −8.86793 | + | 8.86793i | −0.456117 | + | 0.456117i | ||||
\(379\) | −21.2829 | −1.09323 | −0.546614 | − | 0.837384i | \(-0.684084\pi\) | ||||
−0.546614 | + | 0.837384i | \(0.684084\pi\) | |||||||
\(380\) | −0.533302 | + | 1.13379i | −0.0273578 | + | 0.0581623i | ||||
\(381\) | 16.3454 | 0.837398 | ||||||||
\(382\) | 11.8516 | + | 11.8516i | 0.606380 | + | 0.606380i | ||||
\(383\) | 19.7855 | − | 19.7855i | 1.01099 | − | 1.01099i | 0.0110515 | − | 0.999939i | \(-0.496482\pi\) |
0.999939 | − | 0.0110515i | \(-0.00351787\pi\) | |||||||
\(384\) | 21.5685i | 1.10066i | ||||||||
\(385\) | 10.7647 | − | 3.87745i | 0.548619 | − | 0.197613i | ||||
\(386\) | 29.6409 | 1.50868 | ||||||||
\(387\) | −7.33480 | − | 7.33480i | −0.372849 | − | 0.372849i | ||||
\(388\) | −11.4135 | + | 11.4135i | −0.579434 | + | 0.579434i | ||||
\(389\) | 3.47307 | 0.176092 | 0.0880458 | − | 0.996116i | \(-0.471938\pi\) | ||||
0.0880458 | + | 0.996116i | \(0.471938\pi\) | |||||||
\(390\) | −3.53169 | − | 9.80477i | −0.178834 | − | 0.496484i | ||||
\(391\) | −14.0240 | + | 31.3054i | −0.709223 | + | 1.58318i | ||||
\(392\) | −1.85780 | + | 1.85780i | −0.0938328 | + | 0.0938328i | ||||
\(393\) | 3.71383 | + | 3.71383i | 0.187338 | + | 0.187338i | ||||
\(394\) | − | 28.9147i | − | 1.45670i | ||||||
\(395\) | −14.2922 | − | 6.72263i | −0.719119 | − | 0.338252i | ||||
\(396\) | − | 23.9284i | − | 1.20245i | ||||||
\(397\) | −0.590946 | + | 0.590946i | −0.0296588 | + | 0.0296588i | −0.721781 | − | 0.692122i | \(-0.756676\pi\) |
0.692122 | + | 0.721781i | \(0.256676\pi\) | |||||||
\(398\) | −22.8769 | + | 22.8769i | −1.14671 | + | 1.14671i | ||||
\(399\) | 0.218736i | 0.0109505i | ||||||||
\(400\) | 1.10810 | + | 1.33860i | 0.0554051 | + | 0.0669300i | ||||
\(401\) | − | 19.3205i | − | 0.964818i | −0.875946 | − | 0.482409i | \(-0.839762\pi\) | ||
0.875946 | − | 0.482409i | \(-0.160238\pi\) | |||||||
\(402\) | 17.5755 | + | 17.5755i | 0.876586 | + | 0.876586i | ||||
\(403\) | −8.63927 | − | 8.63927i | −0.430352 | − | 0.430352i | ||||
\(404\) | 21.9817i | 1.09363i | ||||||||
\(405\) | −4.77911 | − | 2.24795i | −0.237476 | − | 0.111702i | ||||
\(406\) | 12.1046i | 0.600741i | ||||||||
\(407\) | 4.60027 | − | 4.60027i | 0.228027 | − | 0.228027i | ||||
\(408\) | 16.3759 | − | 16.3759i | 0.810727 | − | 0.810727i | ||||
\(409\) | 31.2804i | 1.54671i | 0.633971 | + | 0.773357i | \(0.281424\pi\) | ||||
−0.633971 | + | 0.773357i | \(0.718576\pi\) | |||||||
\(410\) | 43.0303 | − | 15.4996i | 2.12512 | − | 0.765471i | ||||
\(411\) | 18.7487i | 0.924804i | ||||||||
\(412\) | 31.3930 | + | 31.3930i | 1.54662 | + | 1.54662i | ||||
\(413\) | 0.000902782 | 0 | 0.000902782i | 4.44230e−5 | 0 | 4.44230e-5i | ||||
\(414\) | 6.59536 | − | 14.7227i | 0.324144 | − | 0.723580i | ||||
\(415\) | −21.7518 | + | 7.83505i | −1.06776 | + | 0.384607i | ||||
\(416\) | 10.0652 | 0.493489 | ||||||||
\(417\) | −7.14607 | + | 7.14607i | −0.349944 | + | 0.349944i | ||||
\(418\) | −1.45838 | − | 1.45838i | −0.0713316 | − | 0.0713316i | ||||
\(419\) | 1.14152 | 0.0557668 | 0.0278834 | − | 0.999611i | \(-0.491123\pi\) | ||||
0.0278834 | + | 0.999611i | \(0.491123\pi\) | |||||||
\(420\) | −7.87207 | − | 3.70279i | −0.384118 | − | 0.180678i | ||||
\(421\) | − | 18.4172i | − | 0.897600i | −0.893632 | − | 0.448800i | \(-0.851852\pi\) | ||
0.893632 | − | 0.448800i | \(-0.148148\pi\) | |||||||
\(422\) | 38.6721 | − | 38.6721i | 1.88253 | − | 1.88253i | ||||
\(423\) | −11.9975 | − | 11.9975i | −0.583340 | − | 0.583340i | ||||
\(424\) | −25.8788 | −1.25679 | ||||||||
\(425\) | 3.35432 | − | 35.6058i | 0.162709 | − | 1.72713i | ||||
\(426\) | 42.7360 | 2.07056 | ||||||||
\(427\) | 2.59646 | − | 2.59646i | 0.125652 | − | 0.125652i | ||||
\(428\) | 7.76074 | − | 7.76074i | 0.375130 | − | 0.375130i | ||||
\(429\) | 10.5015 | 0.507018 | ||||||||
\(430\) | 15.1350 | − | 32.1768i | 0.729875 | − | 1.55170i | ||||
\(431\) | − | 1.45198i | − | 0.0699396i | −0.999388 | − | 0.0349698i | \(-0.988867\pi\) | ||
0.999388 | − | 0.0349698i | \(-0.0111335\pi\) | |||||||
\(432\) | 1.35719 | − | 1.35719i | 0.0652978 | − | 0.0652978i | ||||
\(433\) | −23.8615 | + | 23.8615i | −1.14671 | + | 1.14671i | −0.159512 | + | 0.987196i | \(0.550992\pi\) |
−0.987196 | + | 0.159512i | \(0.949008\pi\) | |||||||
\(434\) | −16.6602 | −0.799715 | ||||||||
\(435\) | −13.8193 | + | 4.97774i | −0.662585 | + | 0.238664i | ||||
\(436\) | 5.22740i | 0.250347i | ||||||||
\(437\) | −0.303234 | − | 0.795385i | −0.0145056 | − | 0.0380484i | ||||
\(438\) | −7.74037 | − | 7.74037i | −0.369849 | − | 0.369849i | ||||
\(439\) | 8.93212i | 0.426307i | 0.977019 | + | 0.213153i | \(0.0683734\pi\) | ||||
−0.977019 | + | 0.213153i | \(0.931627\pi\) | |||||||
\(440\) | 28.2822 | − | 10.1873i | 1.34830 | − | 0.485661i | ||||
\(441\) | 1.48129 | 0.0705376 | ||||||||
\(442\) | −19.1275 | − | 19.1275i | −0.909804 | − | 0.909804i | ||||
\(443\) | 19.6554 | + | 19.6554i | 0.933858 | + | 0.933858i | 0.997944 | − | 0.0640861i | \(-0.0204132\pi\) |
−0.0640861 | + | 0.997944i | \(0.520413\pi\) | |||||||
\(444\) | −4.94650 | −0.234750 | ||||||||
\(445\) | −19.7277 | − | 9.27931i | −0.935181 | − | 0.439881i | ||||
\(446\) | 13.7865 | 0.652809 | ||||||||
\(447\) | −17.5121 | − | 17.5121i | −0.828296 | − | 0.828296i | ||||
\(448\) | 9.21354 | − | 9.21354i | 0.435299 | − | 0.435299i | ||||
\(449\) | − | 2.94394i | − | 0.138933i | −0.997584 | − | 0.0694665i | \(-0.977870\pi\) | ||
0.997584 | − | 0.0694665i | \(-0.0221297\pi\) | |||||||
\(450\) | −1.57751 | + | 16.7451i | −0.0743646 | + | 0.789372i | ||||
\(451\) | 46.0882i | 2.17021i | ||||||||
\(452\) | −25.6106 | − | 25.6106i | −1.20462 | − | 1.20462i | ||||
\(453\) | 14.2328 | + | 14.2328i | 0.668718 | + | 0.668718i | ||||
\(454\) | −17.0017 | −0.797931 | ||||||||
\(455\) | −1.58501 | + | 3.36970i | −0.0743063 | + | 0.157974i | ||||
\(456\) | 0.574688i | 0.0269122i | ||||||||
\(457\) | −8.88589 | − | 8.88589i | −0.415664 | − | 0.415664i | 0.468042 | − | 0.883706i | \(-0.344960\pi\) |
−0.883706 | + | 0.468042i | \(0.844960\pi\) | |||||||
\(458\) | 3.42277 | − | 3.42277i | 0.159935 | − | 0.159935i | ||||
\(459\) | −39.5011 | −1.84376 | ||||||||
\(460\) | 33.7583 | + | 2.55133i | 1.57399 | + | 0.118956i | ||||
\(461\) | 13.4101 | 0.624569 | 0.312285 | − | 0.949989i | \(-0.398906\pi\) | ||||
0.312285 | + | 0.949989i | \(0.398906\pi\) | |||||||
\(462\) | 10.1257 | − | 10.1257i | 0.471091 | − | 0.471091i | ||||
\(463\) | 9.58408 | + | 9.58408i | 0.445410 | + | 0.445410i | 0.893825 | − | 0.448415i | \(-0.148011\pi\) |
−0.448415 | + | 0.893825i | \(0.648011\pi\) | |||||||
\(464\) | − | 1.85254i | − | 0.0860022i | ||||||
\(465\) | −6.85112 | − | 19.0202i | −0.317713 | − | 0.882042i | ||||
\(466\) | −33.9761 | −1.57391 | ||||||||
\(467\) | 15.8943 | + | 15.8943i | 0.735499 | + | 0.735499i | 0.971703 | − | 0.236204i | \(-0.0759034\pi\) |
−0.236204 | + | 0.971703i | \(0.575903\pi\) | |||||||
\(468\) | 5.50683 | + | 5.50683i | 0.254553 | + | 0.254553i | ||||
\(469\) | − | 8.88154i | − | 0.410111i | ||||||
\(470\) | 24.7564 | − | 52.6316i | 1.14193 | − | 2.42772i | ||||
\(471\) | − | 18.4781i | − | 0.851427i | ||||||
\(472\) | 0.00237190 | − | 0.00237190i | 0.000109175 | − | 0.000109175i | ||||
\(473\) | 25.3370 | + | 25.3370i | 1.16499 | + | 1.16499i | ||||
\(474\) | −19.7675 | −0.907949 | ||||||||
\(475\) | 0.565910 | + | 0.683625i | 0.0259657 | + | 0.0313669i | ||||
\(476\) | −22.5807 | −1.03498 | ||||||||
\(477\) | 10.3171 | + | 10.3171i | 0.472386 | + | 0.472386i | ||||
\(478\) | 32.4568 | + | 32.4568i | 1.48454 | + | 1.48454i | ||||
\(479\) | −14.2661 | −0.651833 | −0.325917 | − | 0.945398i | \(-0.605673\pi\) | ||||
−0.325917 | + | 0.945398i | \(0.605673\pi\) | |||||||
\(480\) | 15.0708 | + | 7.08886i | 0.687885 | + | 0.323561i | ||||
\(481\) | 2.11739i | 0.0965445i | ||||||||
\(482\) | 6.31786 | + | 6.31786i | 0.287771 | + | 0.287771i | ||||
\(483\) | 5.52247 | − | 2.10539i | 0.251281 | − | 0.0957987i | ||||
\(484\) | 47.9307i | 2.17867i | ||||||||
\(485\) | 3.87442 | + | 10.7563i | 0.175928 | + | 0.488416i | ||||
\(486\) | 31.0135 | 1.40680 | ||||||||
\(487\) | −3.24711 | + | 3.24711i | −0.147140 | + | 0.147140i | −0.776839 | − | 0.629699i | \(-0.783178\pi\) |
0.629699 | + | 0.776839i | \(0.283178\pi\) | |||||||
\(488\) | 6.82174 | − | 6.82174i | 0.308806 | − | 0.308806i | ||||
\(489\) | − | 12.5779i | − | 0.568793i | ||||||
\(490\) | 1.72083 | + | 4.77740i | 0.0777390 | + | 0.215821i | ||||
\(491\) | −20.4635 | −0.923505 | −0.461753 | − | 0.887009i | \(-0.652779\pi\) | ||||
−0.461753 | + | 0.887009i | \(0.652779\pi\) | |||||||
\(492\) | 24.7785 | − | 24.7785i | 1.11710 | − | 1.11710i | ||||
\(493\) | −26.9593 | + | 26.9593i | −1.21418 | + | 1.21418i | ||||
\(494\) | 0.671254 | 0.0302011 | ||||||||
\(495\) | −15.3366 | − | 7.21388i | −0.689329 | − | 0.324240i | ||||
\(496\) | 2.54975 | 0.114487 | ||||||||
\(497\) | −10.7980 | − | 10.7980i | −0.484357 | − | 0.484357i | ||||
\(498\) | −20.4607 | + | 20.4607i | −0.916866 | + | 0.916866i | ||||
\(499\) | 4.19951i | 0.187996i | 0.995572 | + | 0.0939979i | \(0.0299647\pi\) | ||||
−0.995572 | + | 0.0939979i | \(0.970035\pi\) | |||||||
\(500\) | −34.1828 | + | 8.79401i | −1.52870 | + | 0.393280i | ||||
\(501\) | −20.1092 | −0.898414 | ||||||||
\(502\) | −20.9656 | − | 20.9656i | −0.935742 | − | 0.935742i | ||||
\(503\) | 5.36658 | − | 5.36658i | 0.239284 | − | 0.239284i | −0.577270 | − | 0.816554i | \(-0.695882\pi\) |
0.816554 | + | 0.577270i | \(0.195882\pi\) | |||||||
\(504\) | 3.89182 | 0.173355 | ||||||||
\(505\) | 14.0889 | + | 6.62699i | 0.626947 | + | 0.294897i | ||||
\(506\) | −22.7827 | + | 50.8573i | −1.01281 | + | 2.26088i | ||||
\(507\) | 8.91154 | − | 8.91154i | 0.395775 | − | 0.395775i | ||||
\(508\) | −29.6081 | − | 29.6081i | −1.31365 | − | 1.31365i | ||||
\(509\) | 29.0242i | 1.28648i | 0.765666 | + | 0.643238i | \(0.222410\pi\) | ||||
−0.765666 | + | 0.643238i | \(0.777590\pi\) | |||||||
\(510\) | −15.1685 | − | 42.1112i | −0.671674 | − | 1.86472i | ||||
\(511\) | 3.91149i | 0.173034i | ||||||||
\(512\) | −2.77665 | + | 2.77665i | −0.122712 | + | 0.122712i | ||||
\(513\) | 0.693118 | − | 0.693118i | 0.0306019 | − | 0.0306019i | ||||
\(514\) | − | 2.44834i | − | 0.107992i | ||||||
\(515\) | 29.5852 | − | 10.6566i | 1.30368 | − | 0.469587i | ||||
\(516\) | − | 27.2439i | − | 1.19935i | ||||||
\(517\) | 41.4437 | + | 41.4437i | 1.82269 | + | 1.82269i | ||||
\(518\) | 2.04161 | + | 2.04161i | 0.0897033 | + | 0.0897033i | ||||
\(519\) | − | 8.52106i | − | 0.374033i | ||||||
\(520\) | −4.16432 | + | 8.85328i | −0.182618 | + | 0.388242i | ||||
\(521\) | 14.9875i | 0.656613i | 0.944571 | + | 0.328306i | \(0.106478\pi\) | ||||
−0.944571 | + | 0.328306i | \(0.893522\pi\) | |||||||
\(522\) | 12.6787 | − | 12.6787i | 0.554932 | − | 0.554932i | ||||
\(523\) | 9.82258 | − | 9.82258i | 0.429511 | − | 0.429511i | −0.458951 | − | 0.888462i | \(-0.651775\pi\) |
0.888462 | + | 0.458951i | \(0.151775\pi\) | |||||||
\(524\) | − | 13.4545i | − | 0.587763i | ||||||
\(525\) | −4.74650 | + | 3.92919i | −0.207154 | + | 0.171484i | ||||
\(526\) | − | 26.2154i | − | 1.14305i | ||||||
\(527\) | −37.1054 | − | 37.1054i | −1.61634 | − | 1.61634i | ||||
\(528\) | −1.54969 | + | 1.54969i | −0.0674414 | + | 0.0674414i | ||||
\(529\) | −17.1626 | + | 15.3116i | −0.746199 | + | 0.665723i | ||||
\(530\) | −21.2888 | + | 45.2596i | −0.924726 | + | 1.96595i | ||||
\(531\) | −0.00189120 | −8.20712e−5 | ||||||||
\(532\) | 0.396219 | − | 0.396219i | 0.0171783 | − | 0.0171783i | ||||
\(533\) | −10.6066 | − | 10.6066i | −0.459423 | − | 0.459423i | ||||
\(534\) | −27.2852 | −1.18075 | ||||||||
\(535\) | −2.63445 | − | 7.31383i | −0.113897 | − | 0.316204i | ||||
\(536\) | − | 23.3346i | − | 1.00790i | ||||||
\(537\) | 8.21797 | − | 8.21797i | 0.354632 | − | 0.354632i | ||||
\(538\) | 25.9077 | + | 25.9077i | 1.11696 | + | 1.11696i | ||||
\(539\) | −5.11689 | −0.220400 | ||||||||
\(540\) | 13.2114 | + | 36.6778i | 0.568529 | + | 1.57836i | ||||
\(541\) | −4.48296 | −0.192738 | −0.0963688 | − | 0.995346i | \(-0.530723\pi\) | ||||
−0.0963688 | + | 0.995346i | \(0.530723\pi\) | |||||||
\(542\) | −45.0935 | + | 45.0935i | −1.93693 | + | 1.93693i | ||||
\(543\) | 19.4803 | − | 19.4803i | 0.835979 | − | 0.835979i | ||||
\(544\) | 43.2300 | 1.85347 | ||||||||
\(545\) | 3.35043 | + | 1.57594i | 0.143517 | + | 0.0675060i | ||||
\(546\) | 4.66061i | 0.199456i | ||||||||
\(547\) | −17.1333 | + | 17.1333i | −0.732565 | + | 0.732565i | −0.971127 | − | 0.238562i | \(-0.923324\pi\) |
0.238562 | + | 0.971127i | \(0.423324\pi\) | |||||||
\(548\) | 33.9615 | − | 33.9615i | 1.45076 | − | 1.45076i | ||||
\(549\) | −5.43923 | −0.232141 | ||||||||
\(550\) | 5.44928 | − | 57.8435i | 0.232358 | − | 2.46645i | ||||
\(551\) | − | 0.946097i | − | 0.0403051i | ||||||
\(552\) | 14.5093 | − | 5.53154i | 0.617556 | − | 0.235438i | ||||
\(553\) | 4.99461 | + | 4.99461i | 0.212392 | + | 0.212392i | ||||
\(554\) | − | 29.8948i | − | 1.27011i | ||||||
\(555\) | −1.49126 | + | 3.17039i | −0.0633003 | + | 0.134575i | ||||
\(556\) | 25.8889 | 1.09793 | ||||||||
\(557\) | 20.2285 | + | 20.2285i | 0.857111 | + | 0.857111i | 0.990997 | − | 0.133886i | \(-0.0427457\pi\) |
−0.133886 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(558\) | 17.4504 | + | 17.4504i | 0.738734 | + | 0.738734i | ||||
\(559\) | −11.6620 | −0.493248 | ||||||||
\(560\) | −0.263363 | − | 0.731155i | −0.0111291 | − | 0.0308969i | ||||
\(561\) | 45.1038 | 1.90428 | ||||||||
\(562\) | −17.0465 | − | 17.0465i | −0.719064 | − | 0.719064i | ||||
\(563\) | 15.2919 | − | 15.2919i | 0.644478 | − | 0.644478i | −0.307175 | − | 0.951653i | \(-0.599384\pi\) |
0.951653 | + | 0.307175i | \(0.0993838\pi\) | |||||||
\(564\) | − | 44.5629i | − | 1.87644i | ||||||
\(565\) | −24.1358 | + | 8.69375i | −1.01540 | + | 0.365749i | ||||
\(566\) | − | 4.48001i | − | 0.188309i | ||||||
\(567\) | 1.67013 | + | 1.67013i | 0.0701387 | + | 0.0701387i | ||||
\(568\) | −28.3699 | − | 28.3699i | −1.19037 | − | 1.19037i | ||||
\(569\) | 41.2764 | 1.73039 | 0.865197 | − | 0.501431i | \(-0.167193\pi\) | ||||
0.865197 | + | 0.501431i | \(0.167193\pi\) | |||||||
\(570\) | 1.00508 | + | 0.472758i | 0.0420980 | + | 0.0198017i | ||||
\(571\) | 24.3376i | 1.01850i | 0.860619 | + | 0.509249i | \(0.170077\pi\) | ||||
−0.860619 | + | 0.509249i | \(0.829923\pi\) | |||||||
\(572\) | −19.0225 | − | 19.0225i | −0.795371 | − | 0.795371i | ||||
\(573\) | 6.43158 | − | 6.43158i | 0.268683 | − | 0.268683i | ||||
\(574\) | −20.4541 | −0.853737 | ||||||||
\(575\) | 11.8126 | − | 20.8677i | 0.492619 | − | 0.870245i | ||||
\(576\) | −19.3011 | −0.804211 | ||||||||
\(577\) | 2.19429 | − | 2.19429i | 0.0913493 | − | 0.0913493i | −0.659955 | − | 0.751305i | \(-0.729425\pi\) |
0.751305 | + | 0.659955i | \(0.229425\pi\) | |||||||
\(578\) | −54.8543 | − | 54.8543i | −2.28164 | − | 2.28164i | ||||
\(579\) | − | 16.0854i | − | 0.668487i | ||||||
\(580\) | 34.0491 | + | 16.0157i | 1.41381 | + | 0.665014i | ||||
\(581\) | 10.3395 | 0.428956 | ||||||||
\(582\) | 10.1178 | + | 10.1178i | 0.419396 | + | 0.419396i | ||||
\(583\) | −35.6388 | − | 35.6388i | −1.47601 | − | 1.47601i | ||||
\(584\) | 10.2767i | 0.425254i | ||||||||
\(585\) | 5.18971 | − | 1.86934i | 0.214568 | − | 0.0772877i | ||||
\(586\) | 0.685631i | 0.0283232i | ||||||||
\(587\) | 9.71402 | − | 9.71402i | 0.400940 | − | 0.400940i | −0.477624 | − | 0.878564i | \(-0.658502\pi\) |
0.878564 | + | 0.477624i | \(0.158502\pi\) | |||||||
\(588\) | 2.75100 | + | 2.75100i | 0.113449 | + | 0.113449i | ||||
\(589\) | 1.30216 | 0.0536547 | ||||||||
\(590\) | −0.00219703 | − | 0.00609943i | −9.04501e−5 | − | 0.000251110i | ||||
\(591\) | −15.6913 | −0.645454 | ||||||||
\(592\) | −0.312458 | − | 0.312458i | −0.0128419 | − | 0.0128419i | ||||
\(593\) | 16.3366 | + | 16.3366i | 0.670864 | + | 0.670864i | 0.957915 | − | 0.287051i | \(-0.0926750\pi\) |
−0.287051 | + | 0.957915i | \(0.592675\pi\) | |||||||
\(594\) | −64.1717 | −2.63300 | ||||||||
\(595\) | −6.80757 | + | 14.4728i | −0.279083 | + | 0.593326i | ||||
\(596\) | 63.4432i | 2.59873i | ||||||||
\(597\) | 12.4147 | + | 12.4147i | 0.508102 | + | 0.508102i | ||||
\(598\) | −6.46101 | − | 16.9473i | −0.264211 | − | 0.693027i | ||||
\(599\) | − | 26.0786i | − | 1.06554i | −0.846259 | − | 0.532771i | \(-0.821151\pi\) | ||
0.846259 | − | 0.532771i | \(-0.178849\pi\) | |||||||
\(600\) | −12.4706 | + | 10.3232i | −0.509109 | + | 0.421444i | ||||
\(601\) | −9.06689 | −0.369846 | −0.184923 | − | 0.982753i | \(-0.559204\pi\) | ||||
−0.184923 | + | 0.982753i | \(0.559204\pi\) | |||||||
\(602\) | −11.2446 | + | 11.2446i | −0.458297 | + | 0.458297i | ||||
\(603\) | −9.30279 | + | 9.30279i | −0.378839 | + | 0.378839i | ||||
\(604\) | − | 51.5629i | − | 2.09807i | ||||||
\(605\) | 30.7205 | + | 14.4500i | 1.24897 | + | 0.587477i | ||||
\(606\) | 19.4862 | 0.791574 | ||||||||
\(607\) | −26.0129 | + | 26.0129i | −1.05583 | + | 1.05583i | −0.0574853 | + | 0.998346i | \(0.518308\pi\) |
−0.998346 | + | 0.0574853i | \(0.981692\pi\) | |||||||
\(608\) | −0.758548 | + | 0.758548i | −0.0307632 | + | 0.0307632i | ||||
\(609\) | 6.56888 | 0.266185 | ||||||||
\(610\) | −6.31880 | − | 17.5424i | −0.255841 | − | 0.710271i | ||||
\(611\) | −19.0755 | −0.771712 | ||||||||
\(612\) | 23.6517 | + | 23.6517i | 0.956063 | + | 0.956063i | ||||
\(613\) | −5.84020 | + | 5.84020i | −0.235883 | + | 0.235883i | −0.815143 | − | 0.579260i | \(-0.803342\pi\) |
0.579260 | + | 0.815143i | \(0.303342\pi\) | |||||||
\(614\) | − | 67.8952i | − | 2.74003i | ||||||
\(615\) | −8.41127 | − | 23.3516i | −0.339175 | − | 0.941625i | ||||
\(616\) | −13.4437 | −0.541663 | ||||||||
\(617\) | −6.24759 | − | 6.24759i | −0.251519 | − | 0.251519i | 0.570074 | − | 0.821593i | \(-0.306914\pi\) |
−0.821593 | + | 0.570074i | \(0.806914\pi\) | |||||||
\(618\) | 27.8291 | − | 27.8291i | 1.11945 | − | 1.11945i | ||||
\(619\) | 36.2172 | 1.45569 | 0.727846 | − | 0.685741i | \(-0.240522\pi\) | ||||
0.727846 | + | 0.685741i | \(0.240522\pi\) | |||||||
\(620\) | −22.0432 | + | 46.8635i | −0.885276 | + | 1.88208i | ||||
\(621\) | −24.1708 | − | 10.8279i | −0.969940 | − | 0.434507i | ||||
\(622\) | −36.9174 | + | 36.9174i | −1.48025 | + | 1.48025i | ||||
\(623\) | 6.89410 | + | 6.89410i | 0.276206 | + | 0.276206i | ||||
\(624\) | − | 0.713281i | − | 0.0285541i | ||||||
\(625\) | −4.66893 | + | 24.5602i | −0.186757 | + | 0.982406i | ||||
\(626\) | 66.5385i | 2.65941i | ||||||||
\(627\) | −0.791427 | + | 0.791427i | −0.0316065 | + | 0.0316065i | ||||
\(628\) | −33.4714 | + | 33.4714i | −1.33565 | + | 1.33565i | ||||
\(629\) | 9.09412i | 0.362606i | ||||||||
\(630\) | 3.20154 | − | 6.80643i | 0.127553 | − | 0.271175i | ||||
\(631\) | 2.26966i | 0.0903538i | 0.998979 | + | 0.0451769i | \(0.0143851\pi\) | ||||
−0.998979 | + | 0.0451769i | \(0.985615\pi\) | |||||||
\(632\) | 13.1224 | + | 13.1224i | 0.521982 | + | 0.521982i | ||||
\(633\) | −20.9864 | − | 20.9864i | −0.834136 | − | 0.834136i | ||||
\(634\) | 40.2994i | 1.60050i | ||||||||
\(635\) | −27.9031 | + | 10.0507i | −1.10730 | + | 0.398851i | ||||
\(636\) | 38.3210i | 1.51953i | ||||||||
\(637\) | 1.17759 | − | 1.17759i | 0.0466577 | − | 0.0466577i | ||||
\(638\) | −43.7967 | + | 43.7967i | −1.73393 | + | 1.73393i | ||||
\(639\) | 22.6203i | 0.894847i | ||||||||
\(640\) | −13.2624 | − | 36.8194i | −0.524243 | − | 1.45541i | ||||
\(641\) | 34.5031i | 1.36279i | 0.731916 | + | 0.681395i | \(0.238626\pi\) | ||||
−0.731916 | + | 0.681395i | \(0.761374\pi\) | |||||||
\(642\) | −6.87970 | − | 6.87970i | −0.271520 | − | 0.271520i | ||||
\(643\) | 2.18441 | − | 2.18441i | 0.0861445 | − | 0.0861445i | −0.662721 | − | 0.748866i | \(-0.730599\pi\) |
0.748866 | + | 0.662721i | \(0.230599\pi\) | |||||||
\(644\) | −13.8172 | − | 6.18971i | −0.544472 | − | 0.243909i | ||||
\(645\) | −17.4616 | − | 8.21341i | −0.687550 | − | 0.323403i | ||||
\(646\) | 2.88302 | 0.113431 | ||||||||
\(647\) | 20.3831 | − | 20.3831i | 0.801343 | − | 0.801343i | −0.181962 | − | 0.983305i | \(-0.558245\pi\) |
0.983305 | + | 0.181962i | \(0.0582449\pi\) | |||||||
\(648\) | 4.38796 | + | 4.38796i | 0.172375 | + | 0.172375i | ||||
\(649\) | 0.00653288 | 0.000256438 | ||||||||
\(650\) | 12.0579 | + | 14.5660i | 0.472948 | + | 0.571326i | ||||
\(651\) | 9.04110i | 0.354348i | ||||||||
\(652\) | −22.7837 | + | 22.7837i | −0.892279 | + | 0.892279i | ||||
\(653\) | −7.89570 | − | 7.89570i | −0.308983 | − | 0.308983i | 0.535532 | − | 0.844515i | \(-0.320111\pi\) |
−0.844515 | + | 0.535532i | \(0.820111\pi\) | |||||||
\(654\) | 4.63395 | 0.181202 | ||||||||
\(655\) | −8.62349 | − | 4.05623i | −0.336947 | − | 0.158490i | ||||
\(656\) | 3.13039 | 0.122221 | ||||||||
\(657\) | 4.09701 | − | 4.09701i | 0.159840 | − | 0.159840i | ||||
\(658\) | −18.3928 | + | 18.3928i | −0.717028 | + | 0.717028i | ||||
\(659\) | 27.2105 | 1.05997 | 0.529986 | − | 0.848007i | \(-0.322197\pi\) | ||||
0.529986 | + | 0.848007i | \(0.322197\pi\) | |||||||
\(660\) | −15.0853 | − | 41.8800i | −0.587193 | − | 1.63018i | ||||
\(661\) | − | 35.6091i | − | 1.38503i | −0.721402 | − | 0.692517i | \(-0.756502\pi\) | ||
0.721402 | − | 0.692517i | \(-0.243498\pi\) | |||||||
\(662\) | −17.1498 | + | 17.1498i | −0.666546 | + | 0.666546i | ||||
\(663\) | −10.3801 | + | 10.3801i | −0.403128 | + | 0.403128i | ||||
\(664\) | 27.1653 | 1.05422 | ||||||||
\(665\) | −0.134500 | − | 0.373402i | −0.00521569 | − | 0.0144799i | ||||
\(666\) | − | 4.27689i | − | 0.165726i | ||||||
\(667\) | −23.8863 | + | 9.10646i | −0.924883 | + | 0.352604i | ||||
\(668\) | 36.4260 | + | 36.4260i | 1.40936 | + | 1.40936i | ||||
\(669\) | − | 7.48160i | − | 0.289256i | ||||||
\(670\) | −40.8101 | − | 19.1959i | −1.57663 | − | 0.741601i | ||||
\(671\) | 18.7890 | 0.725341 | ||||||||
\(672\) | −5.26670 | − | 5.26670i | −0.203167 | − | 0.203167i | ||||
\(673\) | 10.1461 | + | 10.1461i | 0.391104 | + | 0.391104i | 0.875081 | − | 0.483977i | \(-0.160808\pi\) |
−0.483977 | + | 0.875081i | \(0.660808\pi\) | |||||||
\(674\) | 26.1903 | 1.00881 | ||||||||
\(675\) | 27.4911 | + | 2.58986i | 1.05813 | + | 0.0996838i | ||||
\(676\) | −32.2848 | −1.24172 | ||||||||
\(677\) | 2.40673 | + | 2.40673i | 0.0924982 | + | 0.0924982i | 0.751842 | − | 0.659344i | \(-0.229166\pi\) |
−0.659344 | + | 0.751842i | \(0.729166\pi\) | |||||||
\(678\) | −22.7032 | + | 22.7032i | −0.871909 | + | 0.871909i | ||||
\(679\) | − | 5.11289i | − | 0.196215i | ||||||
\(680\) | −17.8857 | + | 38.0246i | −0.685883 | + | 1.45818i | ||||
\(681\) | 9.22645i | 0.353558i | ||||||||
\(682\) | −60.2798 | − | 60.2798i | −2.30823 | − | 2.30823i | ||||
\(683\) | −1.56458 | − | 1.56458i | −0.0598671 | − | 0.0598671i | 0.676539 | − | 0.736406i | \(-0.263479\pi\) |
−0.736406 | + | 0.676539i | \(0.763479\pi\) | |||||||
\(684\) | −0.830023 | −0.0317367 | ||||||||
\(685\) | −11.5285 | − | 32.0057i | −0.440482 | − | 1.22288i | ||||
\(686\) | − | 2.27089i | − | 0.0867031i | ||||||
\(687\) | −1.85745 | − | 1.85745i | −0.0708663 | − | 0.0708663i | ||||
\(688\) | 1.72093 | − | 1.72093i | 0.0656098 | − | 0.0656098i | ||||
\(689\) | 16.4036 | 0.624928 | ||||||||
\(690\) | 2.26168 | − | 29.9258i | 0.0861008 | − | 1.13926i | ||||
\(691\) | −11.4779 | −0.436638 | −0.218319 | − | 0.975877i | \(-0.570057\pi\) | ||||
−0.218319 | + | 0.975877i | \(0.570057\pi\) | |||||||
\(692\) | −15.4351 | + | 15.4351i | −0.586754 | + | 0.586754i | ||||
\(693\) | 5.35958 | + | 5.35958i | 0.203594 | + | 0.203594i | ||||
\(694\) | − | 50.7244i | − | 1.92547i | ||||||
\(695\) | 7.80490 | − | 16.5931i | 0.296057 | − | 0.629412i | ||||
\(696\) | 17.2585 | 0.654184 | ||||||||
\(697\) | −45.5551 | − | 45.5551i | −1.72552 | − | 1.72552i | ||||
\(698\) | −24.0190 | − | 24.0190i | −0.909132 | − | 0.909132i | ||||
\(699\) | 18.4380i | 0.697389i | ||||||||
\(700\) | 15.7152 | + | 1.48049i | 0.593978 | + | 0.0559571i | ||||
\(701\) | − | 2.19390i | − | 0.0828623i | −0.999141 | − | 0.0414312i | \(-0.986808\pi\) | ||
0.999141 | − | 0.0414312i | \(-0.0131917\pi\) | |||||||
\(702\) | 14.7683 | − | 14.7683i | 0.557394 | − | 0.557394i | ||||
\(703\) | −0.159573 | − | 0.159573i | −0.00601840 | − | 0.00601840i | ||||
\(704\) | 66.6727 | 2.51282 | ||||||||
\(705\) | −28.5619 | − | 13.4347i | −1.07571 | − | 0.505980i | ||||
\(706\) | 17.2583 | 0.649525 | ||||||||
\(707\) | −4.92355 | − | 4.92355i | −0.185169 | − | 0.185169i | ||||
\(708\) | −0.00351228 | − | 0.00351228i | −0.000132000 | − | 0.000132000i | ||||
\(709\) | 8.54997 | 0.321101 | 0.160550 | − | 0.987028i | \(-0.448673\pi\) | ||||
0.160550 | + | 0.987028i | \(0.448673\pi\) | |||||||
\(710\) | −72.9543 | + | 26.2782i | −2.73792 | + | 0.986205i | ||||
\(711\) | − | 10.4630i | − | 0.392393i | ||||||
\(712\) | 18.1130 | + | 18.1130i | 0.678813 | + | 0.678813i | ||||
\(713\) | −12.5337 | − | 32.8760i | −0.469391 | − | 1.23122i | ||||
\(714\) | 20.0172i | 0.749125i | ||||||||
\(715\) | −17.9271 | + | 6.45736i | −0.670435 | + | 0.241492i | ||||
\(716\) | −29.7722 | −1.11264 | ||||||||
\(717\) | 17.6136 | − | 17.6136i | 0.657791 | − | 0.657791i | ||||
\(718\) | 41.7426 | − | 41.7426i | 1.55782 | − | 1.55782i | ||||
\(719\) | − | 7.63458i | − | 0.284722i | −0.989815 | − | 0.142361i | \(-0.954531\pi\) | ||
0.989815 | − | 0.142361i | \(-0.0454694\pi\) | |||||||
\(720\) | −0.489979 | + | 1.04169i | −0.0182604 | + | 0.0388214i | ||||
\(721\) | −14.0631 | −0.523736 | ||||||||
\(722\) | 30.4589 | − | 30.4589i | 1.13356 | − | 1.13356i | ||||
\(723\) | 3.42855 | − | 3.42855i | 0.127509 | − | 0.127509i | ||||
\(724\) | −70.5734 | −2.62284 | ||||||||
\(725\) | 20.5300 | − | 16.9949i | 0.762467 | − | 0.631175i | ||||
\(726\) | 42.4893 | 1.57693 | ||||||||
\(727\) | −4.95055 | − | 4.95055i | −0.183606 | − | 0.183606i | 0.609319 | − | 0.792925i | \(-0.291443\pi\) |
−0.792925 | + | 0.609319i | \(0.791443\pi\) | |||||||
\(728\) | 3.09390 | − | 3.09390i | 0.114668 | − | 0.114668i | ||||
\(729\) | − | 23.9160i | − | 0.885779i | ||||||
\(730\) | 17.9731 | + | 8.45399i | 0.665213 | + | 0.312896i | ||||
\(731\) | −50.0878 | −1.85257 | ||||||||
\(732\) | −10.1016 | − | 10.1016i | −0.373364 | − | 0.373364i | ||||
\(733\) | 5.90811 | − | 5.90811i | 0.218221 | − | 0.218221i | −0.589527 | − | 0.807748i | \(-0.700686\pi\) |
0.807748 | + | 0.589527i | \(0.200686\pi\) | |||||||
\(734\) | 21.2376 | 0.783893 | ||||||||
\(735\) | 2.59258 | − | 0.933852i | 0.0956288 | − | 0.0344456i | ||||
\(736\) | 26.4525 | + | 11.8500i | 0.975051 | + | 0.436797i | ||||
\(737\) | 32.1351 | − | 32.1351i | 1.18371 | − | 1.18371i | ||||
\(738\) | 21.4242 | + | 21.4242i | 0.788636 | + | 0.788636i | ||||
\(739\) | 28.0166i | 1.03061i | 0.857008 | + | 0.515304i | \(0.172321\pi\) | ||||
−0.857008 | + | 0.515304i | \(0.827679\pi\) | |||||||
\(740\) | 8.44413 | − | 3.04159i | 0.310412 | − | 0.111811i | ||||
\(741\) | − | 0.364274i | − | 0.0133819i | ||||||
\(742\) | 15.8166 | − | 15.8166i | 0.580646 | − | 0.580646i | ||||
\(743\) | 32.1148 | − | 32.1148i | 1.17818 | − | 1.17818i | 0.197971 | − | 0.980208i | \(-0.436565\pi\) |
0.980208 | − | 0.197971i | \(-0.0634351\pi\) | |||||||
\(744\) | 23.7538i | 0.870858i | ||||||||
\(745\) | 40.6630 | + | 19.1267i | 1.48978 | + | 0.700748i | ||||
\(746\) | 30.7814i | 1.12699i | ||||||||
\(747\) | −10.8299 | − | 10.8299i | −0.396247 | − | 0.396247i | ||||
\(748\) | −81.7012 | − | 81.7012i | −2.98729 | − | 2.98729i | ||||
\(749\) | 3.47656i | 0.127031i | ||||||||
\(750\) | 7.79566 | + | 30.3021i | 0.284657 | + | 1.10648i | ||||
\(751\) | 17.2167i | 0.628247i | 0.949382 | + | 0.314123i | \(0.101711\pi\) | ||||
−0.949382 | + | 0.314123i | \(0.898289\pi\) | |||||||
\(752\) | 2.81493 | − | 2.81493i | 0.102650 | − | 0.102650i | ||||
\(753\) | −11.3776 | + | 11.3776i | −0.414621 | + | 0.414621i | ||||
\(754\) | − | 20.1585i | − | 0.734130i | ||||||
\(755\) | −33.0485 | − | 15.5451i | −1.20276 | − | 0.565742i | ||||
\(756\) | − | 17.4345i | − | 0.634086i | ||||||
\(757\) | 19.8168 | + | 19.8168i | 0.720254 | + | 0.720254i | 0.968657 | − | 0.248403i | \(-0.0799058\pi\) |
−0.248403 | + | 0.968657i | \(0.579906\pi\) | |||||||
\(758\) | 34.1753 | − | 34.1753i | 1.24130 | − | 1.24130i | ||||
\(759\) | 27.5991 | + | 12.3636i | 1.00178 | + | 0.448771i | ||||
\(760\) | −0.353374 | − | 0.981046i | −0.0128182 | − | 0.0355863i | ||||
\(761\) | 4.09666 | 0.148504 | 0.0742520 | − | 0.997240i | \(-0.476343\pi\) | ||||
0.0742520 | + | 0.997240i | \(0.476343\pi\) | |||||||
\(762\) | −26.2468 | + | 26.2468i | −0.950821 | + | 0.950821i | ||||
\(763\) | −1.17085 | − | 1.17085i | −0.0423877 | − | 0.0423877i | ||||
\(764\) | −23.3004 | −0.842979 | ||||||||
\(765\) | 22.2897 | − | 8.02877i | 0.805885 | − | 0.290281i | ||||
\(766\) | 63.5416i | 2.29585i | ||||||||
\(767\) | −0.00150346 | + | 0.00150346i | −5.42867e−5 | + | 5.42867e-5i | ||||
\(768\) | −11.9251 | − | 11.9251i | −0.430310 | − | 0.430310i | ||||
\(769\) | 2.46165 | 0.0887693 | 0.0443847 | − | 0.999015i | \(-0.485867\pi\) | ||||
0.0443847 | + | 0.999015i | \(0.485867\pi\) | |||||||
\(770\) | −11.0593 | + | 23.5118i | −0.398548 | + | 0.847307i | ||||
\(771\) | −1.32866 | −0.0478504 | ||||||||
\(772\) | −29.1372 | + | 29.1372i | −1.04867 | + | 1.04867i | ||||
\(773\) | 25.8564 | − | 25.8564i | 0.929989 | − | 0.929989i | −0.0677156 | − | 0.997705i | \(-0.521571\pi\) |
0.997705 | + | 0.0677156i | \(0.0215710\pi\) | |||||||
\(774\) | 23.5559 | 0.846699 | ||||||||
\(775\) | 23.3910 | + | 28.2566i | 0.840229 | + | 1.01501i | ||||
\(776\) | − | 13.4332i | − | 0.482223i | ||||||
\(777\) | 1.10794 | − | 1.10794i | 0.0397470 | − | 0.0397470i | ||||
\(778\) | −5.57693 | + | 5.57693i | −0.199943 | + | 0.199943i | ||||
\(779\) | 1.59869 | 0.0572792 | ||||||||
\(780\) | 13.1098 | + | 6.16648i | 0.469407 | + | 0.220795i | ||||
\(781\) | − | 78.1386i | − | 2.79602i | ||||||
\(782\) | −27.7499 | − | 72.7883i | −0.992334 | − | 2.60290i | ||||
\(783\) | −20.8151 | − | 20.8151i | −0.743872 | − | 0.743872i | ||||
\(784\) | 0.347548i | 0.0124124i | ||||||||
\(785\) | 11.3622 | + | 31.5439i | 0.405533 | + | 1.12585i | ||||
\(786\) | −11.9271 | −0.425425 | ||||||||
\(787\) | 4.38436 | + | 4.38436i | 0.156286 | + | 0.156286i | 0.780919 | − | 0.624633i | \(-0.214751\pi\) |
−0.624633 | + | 0.780919i | \(0.714751\pi\) | |||||||
\(788\) | 28.4233 | + | 28.4233i | 1.01254 | + | 1.01254i | ||||
\(789\) | −14.2265 | −0.506476 | ||||||||
\(790\) | 33.7449 | − | 12.1550i | 1.20059 | − | 0.432454i | ||||
\(791\) | 11.4727 | 0.407924 | ||||||||
\(792\) | 14.0813 | + | 14.0813i | 0.500359 | + | 0.500359i | ||||
\(793\) | −4.32405 | + | 4.32405i | −0.153552 | + | 0.153552i | ||||
\(794\) | − | 1.89784i | − | 0.0673518i | ||||||
\(795\) | 24.5613 | + | 11.5529i | 0.871101 | + | 0.409740i | ||||
\(796\) | − | 44.9763i | − | 1.59414i | ||||||
\(797\) | 1.04825 | + | 1.04825i | 0.0371311 | + | 0.0371311i | 0.725429 | − | 0.688297i | \(-0.241642\pi\) |
−0.688297 | + | 0.725429i | \(0.741642\pi\) | |||||||
\(798\) | −0.351238 | − | 0.351238i | −0.0124337 | − | 0.0124337i | ||||
\(799\) | −81.9287 | −2.89843 | ||||||||
\(800\) | −30.0862 | − | 2.83434i | −1.06371 | − | 0.100209i | ||||
\(801\) | − | 14.4422i | − | 0.510289i | ||||||
\(802\) | 31.0241 | + | 31.0241i | 1.09550 | + | 1.09550i | ||||
\(803\) | −14.1525 | + | 14.1525i | −0.499431 | + | 0.499431i | ||||
\(804\) | −34.5537 | −1.21861 | ||||||||
\(805\) | −8.13277 | + | 6.98986i | −0.286642 | + | 0.246360i | ||||
\(806\) | 27.7452 | 0.977284 | ||||||||
\(807\) | 14.0595 | − | 14.0595i | 0.494917 | − | 0.494917i | ||||
\(808\) | −12.9357 | − | 12.9357i | −0.455078 | − | 0.455078i | ||||
\(809\) | 4.06895i | 0.143057i | 0.997439 | + | 0.0715283i | \(0.0227876\pi\) | ||||
−0.997439 | + | 0.0715283i | \(0.977212\pi\) | |||||||
\(810\) | 11.2838 | − | 4.06445i | 0.396473 | − | 0.142810i | ||||
\(811\) | 18.3262 | 0.643521 | 0.321760 | − | 0.946821i | \(-0.395725\pi\) | ||||
0.321760 | + | 0.946821i | \(0.395725\pi\) | |||||||
\(812\) | −11.8989 | − | 11.8989i | −0.417570 | − | 0.417570i | ||||
\(813\) | 24.4712 | + | 24.4712i | 0.858241 | + | 0.858241i | ||||
\(814\) | 14.7739i | 0.517824i | ||||||||
\(815\) | 7.73413 | + | 21.4717i | 0.270915 | + | 0.752120i | ||||
\(816\) | − | 3.06353i | − | 0.107245i | ||||||
\(817\) | 0.878881 | − | 0.878881i | 0.0307482 | − | 0.0307482i | ||||
\(818\) | −50.2289 | − | 50.2289i | −1.75621 | − | 1.75621i | ||||
\(819\) | −2.46688 | −0.0861998 | ||||||||
\(820\) | −27.0629 | + | 57.5354i | −0.945078 | + | 2.00922i | ||||
\(821\) | 35.7546 | 1.24784 | 0.623922 | − | 0.781487i | \(-0.285538\pi\) | ||||
0.623922 | + | 0.781487i | \(0.285538\pi\) | |||||||
\(822\) | −30.1060 | − | 30.1060i | −1.05007 | − | 1.05007i | ||||
\(823\) | −0.789736 | − | 0.789736i | −0.0275285 | − | 0.0275285i | 0.693209 | − | 0.720737i | \(-0.256196\pi\) |
−0.720737 | + | 0.693209i | \(0.756196\pi\) | |||||||
\(824\) | −36.9481 | −1.28715 | ||||||||
\(825\) | −31.3903 | − | 2.95719i | −1.09287 | − | 0.102956i | ||||
\(826\) | 0.00289931i | 0.000100880i | ||||||||
\(827\) | 29.5585 | + | 29.5585i | 1.02785 | + | 1.02785i | 0.999601 | + | 0.0282480i | \(0.00899281\pi\) |
0.0282480 | + | 0.999601i | \(0.491007\pi\) | |||||||
\(828\) | 7.98921 | + | 20.9558i | 0.277644 | + | 0.728264i | ||||
\(829\) | − | 0.156018i | − | 0.00541874i | −0.999996 | − | 0.00270937i | \(-0.999138\pi\) | ||
0.999996 | − | 0.00270937i | \(-0.000862420\pi\) | |||||||
\(830\) | 22.3471 | − | 47.5096i | 0.775678 | − | 1.64908i | ||||
\(831\) | −16.2232 | −0.562776 | ||||||||
\(832\) | −15.3439 | + | 15.3439i | −0.531953 | + | 0.531953i | ||||
\(833\) | 5.05771 | − | 5.05771i | 0.175239 | − | 0.175239i | ||||
\(834\) | − | 22.9498i | − | 0.794686i | ||||||
\(835\) | 34.3283 | − | 12.3651i | 1.18798 | − | 0.427912i | ||||
\(836\) | 2.86719 | 0.0991638 | ||||||||
\(837\) | 28.6490 | − | 28.6490i | 0.990253 | − | 0.990253i | ||||
\(838\) | −1.83301 | + | 1.83301i | −0.0633202 | + | 0.0633202i | ||||
\(839\) | 18.1367 | 0.626150 | 0.313075 | − | 0.949728i | \(-0.398641\pi\) | ||||
0.313075 | + | 0.949728i | \(0.398641\pi\) | |||||||
\(840\) | 6.81154 | − | 2.45353i | 0.235020 | − | 0.0846547i | ||||
\(841\) | 0.587614 | 0.0202625 | ||||||||
\(842\) | 29.5737 | + | 29.5737i | 1.01918 | + | 1.01918i | ||||
\(843\) | −9.25074 | + | 9.25074i | −0.318612 | + | 0.318612i | ||||
\(844\) | 76.0299i | 2.61706i | ||||||||
\(845\) | −9.73314 | + | 20.6925i | −0.334830 | + | 0.711844i | ||||
\(846\) | 38.5304 | 1.32470 | ||||||||
\(847\) | −10.7357 | − | 10.7357i | −0.368883 | − | 0.368883i | ||||
\(848\) | −2.42065 | + | 2.42065i | −0.0831253 | + | 0.0831253i | ||||
\(849\) | −2.43120 | −0.0834384 | ||||||||
\(850\) | 51.7882 | + | 62.5607i | 1.77632 | + | 2.14581i | ||||
\(851\) | −2.49284 | + | 5.56470i | −0.0854533 | + | 0.190756i | ||||
\(852\) | −42.0097 | + | 42.0097i | −1.43923 | + | 1.43923i | ||||
\(853\) | 24.4378 | + | 24.4378i | 0.836734 | + | 0.836734i | 0.988428 | − | 0.151694i | \(-0.0484728\pi\) |
−0.151694 | + | 0.988428i | \(0.548473\pi\) | |||||||
\(854\) | 8.33862i | 0.285342i | ||||||||
\(855\) | −0.250233 | + | 0.531992i | −0.00855779 | + | 0.0181937i | ||||
\(856\) | 9.13404i | 0.312195i | ||||||||
\(857\) | −15.8794 | + | 15.8794i | −0.542431 | + | 0.542431i | −0.924241 | − | 0.381810i | \(-0.875301\pi\) |
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(858\) | −16.8630 | + | 16.8630i | −0.575692 | + | 0.575692i | ||||
\(859\) | − | 34.7748i | − | 1.18650i | −0.805018 | − | 0.593250i | \(-0.797844\pi\) | ||
0.805018 | − | 0.593250i | \(-0.202156\pi\) | |||||||
\(860\) | 16.7522 | + | 46.5079i | 0.571245 | + | 1.58590i | ||||
\(861\) | 11.0999i | 0.378285i | ||||||||
\(862\) | 2.33154 | + | 2.33154i | 0.0794126 | + | 0.0794126i | ||||
\(863\) | −32.0309 | − | 32.0309i | −1.09035 | − | 1.09035i | −0.995491 | − | 0.0948543i | \(-0.969761\pi\) |
−0.0948543 | − | 0.995491i | \(-0.530239\pi\) | |||||||
\(864\) | 33.3777i | 1.13553i | ||||||||
\(865\) | 5.23958 | + | 14.5462i | 0.178151 | + | 0.494587i | ||||
\(866\) | − | 76.6317i | − | 2.60405i | ||||||
\(867\) | −29.7681 | + | 29.7681i | −1.01098 | + | 1.01098i | ||||
\(868\) | 16.3771 | − | 16.3771i | 0.555875 | − | 0.555875i | ||||
\(869\) | 36.1429i | 1.22606i | ||||||||
\(870\) | 14.1975 | − | 30.1836i | 0.481339 | − | 1.02332i | ||||
\(871\) | 14.7910i | 0.501173i | ||||||||
\(872\) | −3.07621 | − | 3.07621i | −0.104173 | − | 0.104173i | ||||
\(873\) | −5.35539 | + | 5.35539i | −0.181253 | + | 0.181253i | ||||
\(874\) | 1.76412 | + | 0.790279i | 0.0596724 | + | 0.0267316i | ||||
\(875\) | 5.68667 | − | 9.62610i | 0.192245 | − | 0.325422i | ||||
\(876\) | 15.2177 | 0.514157 | ||||||||
\(877\) | 2.28214 | − | 2.28214i | 0.0770623 | − | 0.0770623i | −0.667525 | − | 0.744587i | \(-0.732646\pi\) |
0.744587 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(878\) | −14.3429 | − | 14.3429i | −0.484048 | − | 0.484048i | ||||
\(879\) | 0.372076 | 0.0125498 | ||||||||
\(880\) | 1.69256 | − | 3.59836i | 0.0570562 | − | 0.121301i | ||||
\(881\) | − | 43.1349i | − | 1.45325i | −0.687034 | − | 0.726625i | \(-0.741088\pi\) | ||
0.687034 | − | 0.726625i | \(-0.258912\pi\) | |||||||
\(882\) | −2.37860 | + | 2.37860i | −0.0800916 | + | 0.0800916i | ||||
\(883\) | 0.0867921 | + | 0.0867921i | 0.00292079 | + | 0.00292079i | 0.708566 | − | 0.705645i | \(-0.249343\pi\) |
−0.705645 | + | 0.708566i | \(0.749343\pi\) | |||||||
\(884\) | 37.6050 | 1.26479 | ||||||||
\(885\) | −0.00331002 | + | 0.00119227i | −0.000111265 | + | 4.00779e-5i | ||||
\(886\) | −63.1240 | −2.12069 | ||||||||
\(887\) | 8.94261 | − | 8.94261i | 0.300264 | − | 0.300264i | −0.540853 | − | 0.841117i | \(-0.681899\pi\) |
0.841117 | + | 0.540853i | \(0.181899\pi\) | |||||||
\(888\) | 2.91090 | − | 2.91090i | 0.0976834 | − | 0.0976834i | ||||
\(889\) | 13.2635 | 0.444842 | ||||||||
\(890\) | 46.5783 | − | 16.7776i | 1.56131 | − | 0.562386i | ||||
\(891\) | 12.0857i | 0.404885i | ||||||||
\(892\) | −13.5522 | + | 13.5522i | −0.453762 | + | 0.453762i | ||||
\(893\) | 1.43759 | − | 1.43759i | 0.0481070 | − | 0.0481070i | ||||
\(894\) | 56.2407 | 1.88097 | ||||||||
\(895\) | −8.97563 | + | 19.0821i | −0.300022 | + | 0.637843i | ||||
\(896\) | 17.5018i | 0.584693i | ||||||||
\(897\) | −9.19690 | + | 3.50624i | −0.307076 | + | 0.117070i | ||||
\(898\) | 4.72727 | + | 4.72727i | 0.157751 | + | 0.157751i | ||||
\(899\) | − | 39.1055i | − | 1.30424i | ||||||
\(900\) | −14.9098 | − | 18.0113i | −0.496995 | − | 0.600375i | ||||
\(901\) | 70.4532 | 2.34714 | ||||||||
\(902\) | −74.0068 | − | 74.0068i | −2.46416 | − | 2.46416i | ||||
\(903\) | 6.10219 | + | 6.10219i | 0.203068 | + | 0.203068i | ||||
\(904\) | 30.1425 | 1.00253 | ||||||||
\(905\) | −21.2763 | + | 45.2330i | −0.707247 | + | 1.50360i | ||||
\(906\) | −45.7092 | −1.51859 | ||||||||
\(907\) | 36.4687 | + | 36.4687i | 1.21092 | + | 1.21092i | 0.970724 | + | 0.240198i | \(0.0772123\pi\) |
0.240198 | + | 0.970724i | \(0.422788\pi\) | |||||||
\(908\) | 16.7128 | − | 16.7128i | 0.554635 | − | 0.554635i | ||||
\(909\) | 10.3141i | 0.342099i | ||||||||
\(910\) | −2.86580 | − | 7.95609i | −0.0950002 | − | 0.263742i | ||||
\(911\) | − | 19.8492i | − | 0.657632i | −0.944394 | − | 0.328816i | \(-0.893350\pi\) | ||
0.944394 | − | 0.328816i | \(-0.106650\pi\) | |||||||
\(912\) | 0.0537551 | + | 0.0537551i | 0.00178001 | + | 0.00178001i | ||||
\(913\) | 37.4104 | + | 37.4104i | 1.23810 | + | 1.23810i | ||||
\(914\) | 28.5373 | 0.943929 | ||||||||
\(915\) | −9.51984 | + | 3.42906i | −0.314716 | + | 0.113361i | ||||
\(916\) | 6.72921i | 0.222339i | ||||||||
\(917\) | 3.01359 | + | 3.01359i | 0.0995177 | + | 0.0995177i | ||||
\(918\) | 63.4295 | − | 63.4295i | 2.09349 | − | 2.09349i | ||||
\(919\) | −24.4110 | −0.805243 | −0.402621 | − | 0.915367i | \(-0.631901\pi\) | ||||
−0.402621 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(920\) | −21.3674 | + | 18.3646i | −0.704462 | + | 0.605462i | ||||
\(921\) | −36.8451 | −1.21409 | ||||||||
\(922\) | −21.5334 | + | 21.5334i | −0.709165 | + | 0.709165i | ||||
\(923\) | 17.9826 | + | 17.9826i | 0.591905 | + | 0.591905i | ||||
\(924\) | 19.9073i | 0.654902i | ||||||||
\(925\) | 0.596249 | − | 6.32912i | 0.0196045 | − | 0.208100i | ||||
\(926\) | −30.7795 | −1.01148 | ||||||||
\(927\) | 14.7301 | + | 14.7301i | 0.483799 | + | 0.483799i | ||||
\(928\) | 22.7801 | + | 22.7801i | 0.747792 | + | 0.747792i | ||||
\(929\) | − | 3.50894i | − | 0.115124i | −0.998342 | − | 0.0575622i | \(-0.981667\pi\) | ||
0.998342 | − | 0.0575622i | \(-0.0183328\pi\) | |||||||
\(930\) | 41.5433 | + | 19.5407i | 1.36226 | + | 0.640766i | ||||
\(931\) | 0.177493i | 0.00581711i | ||||||||
\(932\) | 33.3987 | − | 33.3987i | 1.09401 | − | 1.09401i | ||||
\(933\) | 20.0342 | + | 20.0342i | 0.655891 | + | 0.655891i | ||||
\(934\) | −51.0449 | −1.67024 | ||||||||
\(935\) | −76.9963 | + | 27.7342i | −2.51805 | + | 0.907006i | ||||
\(936\) | −6.48128 | −0.211847 | ||||||||
\(937\) | 43.0451 | + | 43.0451i | 1.40622 | + | 1.40622i | 0.778181 | + | 0.628040i | \(0.216143\pi\) |
0.628040 | + | 0.778181i | \(0.283857\pi\) | |||||||
\(938\) | 14.2617 | + | 14.2617i | 0.465660 | + | 0.465660i | ||||
\(939\) | 36.1089 | 1.17837 | ||||||||
\(940\) | 27.4016 | + | 76.0730i | 0.893742 | + | 2.48123i | ||||
\(941\) | − | 0.196834i | − | 0.00641659i | −0.999995 | − | 0.00320830i | \(-0.998979\pi\) | ||
0.999995 | − | 0.00320830i | \(-0.00102123\pi\) | |||||||
\(942\) | 29.6715 | + | 29.6715i | 0.966750 | + | 0.966750i | ||||
\(943\) | −15.3879 | − | 40.3626i | −0.501099 | − | 1.31439i | ||||
\(944\) | 0 | 0.000443724i | 0 | 1.44420e-5i | ||||||
\(945\) | −11.1744 | − | 5.25610i | −0.363503 | − | 0.170981i | ||||
\(946\) | −81.3704 | −2.64558 | ||||||||
\(947\) | −26.8664 | + | 26.8664i | −0.873040 | + | 0.873040i | −0.992803 | − | 0.119763i | \(-0.961787\pi\) |
0.119763 | + | 0.992803i | \(0.461787\pi\) | |||||||
\(948\) | 19.4315 | − | 19.4315i | 0.631107 | − | 0.631107i | ||||
\(949\) | − | 6.51404i | − | 0.211455i | ||||||
\(950\) | −2.00646 | − | 0.189023i | −0.0650981 | − | 0.00613271i | ||||
\(951\) | 21.8696 | 0.709169 | ||||||||
\(952\) | 13.2882 | − | 13.2882i | 0.430674 | − | 0.430674i | ||||
\(953\) | −3.37953 | + | 3.37953i | −0.109474 | + | 0.109474i | −0.759722 | − | 0.650248i | \(-0.774665\pi\) |
0.650248 | + | 0.759722i | \(0.274665\pi\) | |||||||
\(954\) | −33.1335 | −1.07274 | ||||||||
\(955\) | −7.02454 | + | 14.9341i | −0.227309 | + | 0.483255i | ||||
\(956\) | −63.8106 | −2.06378 | ||||||||
\(957\) | 23.7675 | + | 23.7675i | 0.768293 | + | 0.768293i | ||||
\(958\) | 22.9079 | − | 22.9079i | 0.740122 | − | 0.740122i | ||||
\(959\) | 15.2136i | 0.491274i | ||||||||
\(960\) | −33.7811 | + | 12.1680i | −1.09028 | + | 0.392721i | ||||
\(961\) | 22.8229 | 0.736222 | ||||||||
\(962\) | −3.40002 | − | 3.40002i | −0.109621 | − | 0.109621i | ||||
\(963\) | 3.64145 | − | 3.64145i | 0.117344 | − | 0.117344i | ||||
\(964\) | −12.4210 | −0.400053 | ||||||||
\(965\) | 9.89089 | + | 27.4593i | 0.318399 | + | 0.883947i | ||||
\(966\) | −5.48702 | + | 12.2485i | −0.176542 | + | 0.394091i | ||||
\(967\) | −37.8515 | + | 37.8515i | −1.21722 | + | 1.21722i | −0.248622 | + | 0.968601i | \(0.579978\pi\) |
−0.968601 | + | 0.248622i | \(0.920022\pi\) | |||||||
\(968\) | −28.2061 | − | 28.2061i | −0.906580 | − | 0.906580i | ||||
\(969\) | − | 1.56455i | − | 0.0502605i | ||||||
\(970\) | −23.4934 | − | 11.0506i | −0.754328 | − | 0.354813i | ||||
\(971\) | 30.5794i | 0.981339i | 0.871346 | + | 0.490670i | \(0.163248\pi\) | ||||
−0.871346 | + | 0.490670i | \(0.836752\pi\) | |||||||
\(972\) | −30.4865 | + | 30.4865i | −0.977854 | + | 0.977854i | ||||
\(973\) | −5.79869 | + | 5.79869i | −0.185897 | + | 0.185897i | ||||
\(974\) | − | 10.4282i | − | 0.334140i | ||||||
\(975\) | 7.90464 | − | 6.54351i | 0.253151 | − | 0.209560i | ||||
\(976\) | − | 1.27618i | − | 0.0408496i | ||||||
\(977\) | −36.2012 | − | 36.2012i | −1.15818 | − | 1.15818i | −0.984867 | − | 0.173313i | \(-0.944553\pi\) |
−0.173313 | − | 0.984867i | \(-0.555447\pi\) | |||||||
\(978\) | 20.1972 | + | 20.1972i | 0.645834 | + | 0.645834i | ||||
\(979\) | 49.8883i | 1.59444i | ||||||||
\(980\) | −6.38780 | − | 3.00463i | −0.204051 | − | 0.0959794i | ||||
\(981\) | 2.45277i | 0.0783110i | ||||||||
\(982\) | 32.8596 | − | 32.8596i | 1.04859 | − | 1.04859i | ||||
\(983\) | −5.47146 | + | 5.47146i | −0.174512 | + | 0.174512i | −0.788959 | − | 0.614446i | \(-0.789379\pi\) |
0.614446 | + | 0.788959i | \(0.289379\pi\) | |||||||
\(984\) | 29.1631i | 0.929686i | ||||||||
\(985\) | 26.7865 | − | 9.64854i | 0.853489 | − | 0.307428i | ||||
\(986\) | − | 86.5804i | − | 2.75728i | ||||||
\(987\) | 9.98136 | + | 9.98136i | 0.317710 | + | 0.317710i | ||||
\(988\) | −0.659847 | + | 0.659847i | −0.0209925 | + | 0.0209925i | ||||
\(989\) | −30.6488 | − | 13.7298i | −0.974575 | − | 0.436583i | ||||
\(990\) | 36.2107 | − | 13.0432i | 1.15085 | − | 0.414539i | ||||
\(991\) | 10.7653 | 0.341972 | 0.170986 | − | 0.985273i | \(-0.445305\pi\) | ||||
0.170986 | + | 0.985273i | \(0.445305\pi\) | |||||||
\(992\) | −31.3534 | + | 31.3534i | −0.995471 | + | 0.995471i | ||||
\(993\) | 9.30680 | + | 9.30680i | 0.295342 | + | 0.295342i | ||||
\(994\) | 34.6781 | 1.09992 | ||||||||
\(995\) | −28.8269 | − | 13.5593i | −0.913875 | − | 0.429860i | ||||
\(996\) | − | 40.2260i | − | 1.27461i | ||||||
\(997\) | 17.2471 | − | 17.2471i | 0.546220 | − | 0.546220i | −0.379125 | − | 0.925345i | \(-0.623775\pi\) |
0.925345 | + | 0.379125i | \(0.123775\pi\) | |||||||
\(998\) | −6.74341 | − | 6.74341i | −0.213459 | − | 0.213459i | ||||
\(999\) | −7.02154 | −0.222152 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 805.2.l.a.183.7 | yes | 144 | |
5.2 | odd | 4 | inner | 805.2.l.a.22.8 | yes | 144 | |
23.22 | odd | 2 | inner | 805.2.l.a.183.8 | yes | 144 | |
115.22 | even | 4 | inner | 805.2.l.a.22.7 | ✓ | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.l.a.22.7 | ✓ | 144 | 115.22 | even | 4 | inner | |
805.2.l.a.22.8 | yes | 144 | 5.2 | odd | 4 | inner | |
805.2.l.a.183.7 | yes | 144 | 1.1 | even | 1 | trivial | |
805.2.l.a.183.8 | yes | 144 | 23.22 | odd | 2 | inner |